Answer
$\frac{4\pi}{9}, \frac{8\pi}{9},\frac{16\pi}{9}$
Work Step by Step
$sec(\frac{3\theta}{2})=-2$,
$cos(\frac{3\theta}{2})=-\frac{1}{2}$,
$\frac{3\theta}{2}=2k\pi+\frac{2\pi}{3}$ or $2k\pi+\frac{4\pi}{3}$
$\theta=\frac{4k\pi}{3}+\frac{4\pi}{9}$ or $\frac{4k\pi}{3}+\frac{8\pi}{9}$ (k is an integer),
$\theta=\frac{4\pi}{9}, \frac{8\pi}{9},\frac{16\pi}{9}$ in $[0,2\pi)$.
