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