Answer
$4k\pi+\frac{8\pi}{3}, 4k\pi+\frac{10\pi}{3}$.
$\frac{8\pi}{3}, \frac{10\pi}{3}, \frac{20\pi}{3}, \frac{22\pi}{3},\frac{32\pi}{3}, \frac{34\pi}{3}$
Work Step by Step
Using trigonometric identities, we have
$sin(\frac{\theta}{2})=-\frac{\sqrt 3}{2} \longrightarrow \frac{\theta}{2}=2k\pi+\frac{4\pi}{3}, 2k\pi+\frac{5\pi}{3}, \longrightarrow \theta=4k\pi+\frac{8\pi}{3}, 4k\pi+\frac{10\pi}{3}$.
Six examples $\theta=\frac{8\pi}{3}, \frac{10\pi}{3}, \frac{20\pi}{3}, \frac{22\pi}{3},\frac{32\pi}{3}, \frac{34\pi}{3}$