Answer
$\theta=\frac{4\pi}{3}+2k\pi$ and $\theta=\frac{5\pi}{3}+2k\pi$
Six example solutions for $k=0,\pm1$:
$-\frac{2\pi}{3}, -\frac{\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3}, \frac{10\pi}{3}, \frac{11\pi}{3}, $
Work Step by Step
Given $sin\theta=-\frac{\sqrt 3}{2}$,
we can find two $\theta$ values in $[0,2\pi],$ $\theta=\frac{4\pi}{3}, \frac{5\pi}{3},$
and the general solutions are $\theta=\frac{4\pi}{3}+2k\pi$ and $\theta=\frac{5\pi}{3}+2k\pi$
where $k$ is any integer. Six example solutions for $k=0,\pm1$:
$-\frac{2\pi}{3}, -\frac{\pi}{3}, \frac{4\pi}{3}, \frac{5\pi}{3}, \frac{10\pi}{3}, \frac{11\pi}{3}, $
