Answer
$\frac{\pi}{6}+k\pi$, $\frac{5\pi}{6}+k\pi$
Work Step by Step
$\csc^2\theta-4=0$
$\csc^2\theta=4$
$\csc\theta=\pm 2$
$\sin\theta=\pm\frac{1}{2}$
If $\sin\theta=\frac{1}{2}$, then $\theta=\frac{\pi}{6}+2k\pi$ or $\theta=\frac{5\pi}{6}+2k\pi$.
If $\sin\theta=-\frac{1}{2}$, then $\theta=\frac{7\pi}{6}+2k\pi$ or $\theta=\frac{11\pi}{6}+2k\pi$.
Combining these two cases, we get $\theta=\frac{\pi}{6}+k\pi$ or $\theta=\frac{5\pi}{6}+k\pi$.
