Answer
$\theta=k\pi+\frac{3\pi}{4}$ (k is an integer),
$\theta=\frac{3\pi}{4}, \frac{7\pi}{4},\frac{11\pi}{4},\frac{15\pi}{4},\frac{19\pi}{4},\frac{23\pi}{4}$.
Work Step by Step
$sin(2\theta)=-1$,
$2\theta=2k\pi+\frac{3\pi}{2}$
$\theta=k\pi+\frac{3\pi}{4}$ (k is an integer),
Six examples: $\theta=\frac{3\pi}{4}, \frac{7\pi}{4},\frac{11\pi}{4},\frac{15\pi}{4},\frac{19\pi}{4},\frac{23\pi}{4}$.
