\documentclass{standalone}
\standaloneconfig{margin=1cm}
\usepackage{fontspec}
\usepackage{tikz}
\usepackage{xcolor}
\usepackage{amsmath, amsfonts, amssymb, amsthm}
\usetikzlibrary{calc}
\usetikzlibrary{shapes,decorations.text}

\definecolor{RoyalBlue}{HTML}{4169E1} % Royal Blue
\definecolor{ocre}{RGB}{243,102,25} % orange color
\definecolor{DarkGreen}{HTML}{006400} % Dark Green

\begin{document}
\begin{tikzpicture}[]
	    \def\radius{1.5} %
	    \coordinate (O) at (0,0);
	    \coordinate (I) at (\radius,0);
	    \coordinate (M) at (30:\radius);
	    \coordinate (M') at (150:\radius);
	    \node[above left ] at (O) {$O$};
	    \node[above right] at (I) {$I$};
	    \fill (O) circle (1.5pt);
      \draw (O) circle (\radius);
      \draw[] (-1.2*\radius,0) -- (1.2*\radius,0);
      \draw[] (0,-1.2*\radius) -- (0,1.2*\radius);
      \draw[red, line width=0.2mm] ($(M)!1.2!(M')$) --  ($(M')!1.2!(M)$) ;
      \draw[red, line width=0.7mm] (M) arc(30:-210:\radius);
      \foreach \x in {0.75,0.67 , ...,-1.5} {
        \draw[RoyalBlue, thick] (-0.08,\x) -- ++(0.16,0); %
      }

	    \fill (M) circle (1.5pt);
	    \fill (M') circle (1.5pt);

      \node[ above right, font=\small] at (M) {$M\left(\frac{\pi}{6}\right)$};
      \node[ above left, font=\small] at (M') {$M'\left(\frac{5\pi}{6}\right)$};

      \node[above , font=\tiny] at (0.1,0.5*\radius) {$\frac{1}{2}$};
	    \fill (0,0.5*\radius) circle (1.5pt);
      \node[above left, font=\small] at (-\radius,0) {$\pi$};
      \node[below left, font=\small] at (-\radius,0) {$-\pi$};
      \node at (0,-4) {
          \begin{tikzpicture}
            \clip (-7,-3) rectangle (4,3);
            \pgfmathsetmacro{\mypi}{3.14159/1.2} % Define π
            \coordinate (O) at (0,0); % Origin
            \draw[thick,black] (-7,0) -- (3,0); % Draw the main line
            % Loop over intervals
            \foreach \k/\mycolor in {-1/red,0/RoyalBlue}{%
                \pgfmathsetmacro{\start}{-1*\mypi + 2*\k*\mypi} % Start of the interval
                \pgfmathsetmacro{\end}{\mypi/6 + 2*\k*\mypi} % End of the interval
                \pgfmathsetmacro{\mid}{(\start+\end)/2} % End of the interval
                \pgfmathsetmacro{\sstart}{5*\mypi/6 + 2*\k*\mypi} % Start of the interval
                \pgfmathsetmacro{\send}{\mypi+ 2*\k*\mypi} % End of the interval

                \fill[\mycolor] ({\start},0) circle (2pt); %
                \fill[\mycolor] ({\end},0) circle (2pt); %
                \node[\mycolor, font=\Large]  at ({\start},0) {$[$}; %
                \node[\mycolor, font=\Large]  at ({\sstart},0) {$[$}; %
                \node[\mycolor, font=\Large]  at ({\end},0) {$]$}; %
                \node[\mycolor, font=\Large]  at ({\send},0) {$]$}; %
                \node[\mycolor,rotate=90, font=\small] at ({\start},-1.3) {$-\pi+2(\k)\pi$}; %
                \node[\mycolor,rotate=90, font=\small] at ({\end},-1.3) {$\frac{\pi}{6}+2(\k)\pi$}; %
                \node[\mycolor,rotate=90, font=\small] at ({\sstart},1.3) {$\frac{5\pi}{6}+2(\k)\pi$}; %
                \node[\mycolor,rotate=90, font=\small] at ({\send},1.3) {$\pi+2(\k)\pi$}; %
                \node[\mycolor, above] at ({\mid},0.3) {$k=\k$}; %


                % Generate dashed interval points
                \foreach \x in {0, 0.1, ..., 100}{ % This generates a numerical loop
                    \pgfmathsetmacro{\current}{\start + \x}
                    \ifdim \current pt<\end pt % Check if we’re still within bounds
                        \pgfmathsetmacro{\MIN}{-4*\mypi/3-\mypi}
                        \ifdim \MIN pt<\current pt % Check if we’re still within bounds
                            \draw[\mycolor, thick] (\current,-0.1) -- ++(0.1,0.2);
                        \fi
                    \else
                        \breakforeach % Exit the loop when exceeding bounds
                    \fi
                }
                %
                \foreach \x in {0, 0.1, ..., 100}{ % This generates a numerical loop
                    \pgfmathsetmacro{\current}{\sstart + \x}
                    \ifdim \current pt<\send pt % Check if we’re still within bounds
                        \draw[\mycolor, thick] (\current,-0.1) -- ++(0.1,0.2);
                    \else
                        \breakforeach % Exit the loop when exceeding bounds
                    \fi
                }
            }
            % Mark points
            \fill ({-4*\mypi/3},0) circle (2.5pt); % Point at -π
            \fill ({2*\mypi/3},0) circle (2.5pt); % Point at 3π
            \node[below] at ({-4*\mypi/3},0) {$\frac{-4\pi}{3}$};
            \node[below] at ({2*\mypi/3},0) {$\frac{2\pi}{3}$};
        \end{tikzpicture}
      };
      \node[align=left, text width=12cm] at (0,6.5) {Résoudre: ~$x\in[-\pi,\pi]\quad \sin\left(x-\frac{\pi}{3}\right)\le \frac{1}{2}$~};
      \node[align=left, text width=12cm] at (0,5.5) {On pose ~$t=x-\frac{\pi}{3}$~ càd ~$x=t+\frac{\pi}{3}$~};
      \node[align=left, text width=12cm] at (0,4.5) {et puisque ~$x\in[-\pi,\pi]$~ càd ~$x-\frac{\pi}{3}\in\left[-\frac{4\pi}{3},\frac{2\pi}{3}\right]$~};
      \node[align=left, text width=12cm] at (0,3.5) {Ainsi ~$t\in \left[-\frac{4\pi}{3},\frac{2\pi}{3}\right]$~~ ~$\sin t \le \frac{1}{2}$~};
      \node[align=left, text width=12cm] at (0,-7) {Alors ~$t\in\left[\frac{-7\pi}{6},\frac{\pi}{6}\right]$};
      \node[align=left, text width=12cm] at (0,-8) {càd ~$x=t+\frac{\pi}{3}\in\left[\frac{-5\pi}{6},\frac{\pi}{2}\right]$~};
      \node[align=left, text width=12cm] at (0,-9) {Donc ~$S=\left[\frac{-5\pi}{6},\frac{\pi}{2}\right]$~};
      \node at (3.5,5.5) {
          \begin{tikzpicture}
          \coordinate (A) at (0,0);
          \draw[red!50] (A) circle (1.9cm);
          % Draw the inner circle
          \draw[red!50] (A) circle (1.4cm);
          % Draw the curved line
          \draw[red!50, decorate, decoration={text along path,
            text={|\fontspec{DejaVu Sans}\color{red!75}\bfseries|★MOSAID RADOUAN★},
            text align={align=center}, raise=-3pt}] (A) ++ (180:1.6cm) arc (180:0:1.6cm);
          \draw[decorate, decoration={text along path,
            text={|\fontspec{DejaVu Sans}\color{red!75}\bfseries|∞★~mosaid.xyz~★∞ },
            text align={align=center}, raise=-6.5pt}] (A) ++ (180:1.53cm) arc (-180:0:1.53cm);
          \node[red!75,font=\fontsize{48}{48}\fontspec{DejaVu Sans}\bfseries\selectfont] at (A) {✷};
          \end{tikzpicture}

      };
\end{tikzpicture}

\end{document}