Answer
$\theta=\frac{5\pi}{6}+2k\pi$ and $\theta=\frac{7\pi}{6}+2k\pi$
Six example solutions: $-\frac{7\pi}{6}, -\frac{5\pi}{6}, \frac{5\pi}{6},\frac{7\pi}{6},\frac{17\pi}{6},\frac{19\pi}{6}$
Work Step by Step
Given $cos\theta=-\frac{\sqrt 3}{2}$,
we can find two $\theta$ values in $[0,2\pi],$ $\theta=\frac{5\pi}{6}, \frac{7\pi}{6},$
and the general solutions are $\theta=\frac{5\pi}{6}+2k\pi$ and $\theta=\frac{7\pi}{6}+2k\pi$
where $k$ is any integer.
Six example solutions: $-\frac{7\pi}{6}, -\frac{5\pi}{6}, \frac{5\pi}{6},\frac{7\pi}{6},\frac{17\pi}{6},\frac{19\pi}{6}$
