Answer
$\left\{\dfrac{\pi}{2}, \dfrac{7\pi}{6}, \dfrac{11\pi}{6}\right\}$
Work Step by Step
$\sin(3\theta)=-1$
$3\theta=\frac{3}{2}\pi+2k\pi$
$\theta=\frac{1}{2}\pi+\frac{2}{3}k\pi$
Those solutions where $0\le\theta\lt2\pi$ are only:
$\theta=\frac{1}{2}\pi+\frac{2}{3}(0)\pi=\frac{1}{2}\pi$
$\theta=\frac{1}{2}\pi+\frac{2}{3}(1)\pi=\frac{7}{6}\pi$
$\theta=\frac{1}{2}\pi+\frac{2}{3}(2)\pi=\frac{11}{6}\pi$