Answer:Final answer is [tex]x=\frac{\pi}{3}[/tex] and [tex]x=\frac{5\pi}{3}[/tex].Step-by-step explanation:Given equation is [tex]1-\cos\left(\theta\right)=\frac{1}{2}[/tex]Now we need to find the solution of [tex]1-\cos\left(\theta\right)=\frac{1}{2}[/tex] in given interval [tex][0, 2\pi ][/tex].[tex]1-\cos\left(\theta\right)=\frac{1}{2}[/tex][tex]-\cos\left(\theta\right)=\frac{1}{2}-1[/tex][tex]-\cos\left(\theta\right)=-\frac{1}{2}[/tex][tex]\cos\left(\theta\right)=\frac{1}{2}[/tex]which gives [tex]x=\frac{\pi}{3}[/tex] and [tex]x=\frac{5\pi}{3}[/tex] in the given interval.Hence final answer is [tex]x=\frac{\pi}{3}[/tex] and [tex]x=\frac{5\pi}{3}[/tex].