Answer
$2k\pi+\frac{5\pi}{6},2k\pi+\frac{7\pi}{6}$,
$\frac{5\pi}{6}, \frac{7\pi}{6}, \frac{17\pi}{6}, \frac{19\pi}{6}, \frac{29\pi}{6}, \frac{31\pi}{6}$
Work Step by Step
Using trigonometric identities, we have
$cos(\theta)=-\frac{\sqrt 3}{2} \longrightarrow \theta=2k\pi+\frac{5\pi}{6},2k\pi+\frac{7\pi}{6}$.
Six examples $\theta=\frac{5\pi}{6}, \frac{7\pi}{6}, \frac{17\pi}{6}, \frac{19\pi}{6}, \frac{29\pi}{6}, \frac{31\pi}{6}$