Answer
$\frac{\pi}{3}$, $\frac{2\pi}{3}$, $\frac{4\pi}{3}$, $\frac{5\pi}{3}$
Work Step by Step
$2\sin^2\theta=2+\cos2\theta$
$2\sin^2\theta=2+1-2\sin^2\theta$
$4\sin^2\theta=3$
$\sin^2\theta=\frac{3}{4}$
$\sin\theta=\pm\frac{\sqrt{3}}{2}$
If $\sin\theta=\frac{\sqrt{3}}{2}$, the only solutions for $\theta$ in $[0, 2\pi)$ are $\frac{\pi}{3}$ and $\frac{2\pi}{3}$.
If $\sin\theta=-\frac{\sqrt{3}}{2}$, the only solutions for $\theta$ in $[0, 2\pi)$ are $\frac{4\pi}{3}$ and $\frac{5\pi}{3}$.
