Answer
$\frac{\pi}{3}$, $\frac{2\pi}{3}$
Work Step by Step
$\sin 2\theta\cos \theta-\cos 2\theta\sin \theta=\frac{\sqrt{3}}{2}$
$\sin (2\theta-\theta)=\frac{\sqrt{3}}{2}$
$\sin \theta=\frac{\sqrt{3}}{2}$
The only solutions in $[0, 2\pi)$ are $\frac{\pi}{3}$ and $\frac{2\pi}{3}$.
