Answer
$k\pi+\frac{3\pi}{4}$.
$\frac{3\pi}{4}, \frac{7\pi}{4}, \frac{11\pi}{4}, \frac{15\pi}{4}, \frac{19\pi}{4}, \frac{23\pi}{4}$
Work Step by Step
Using trigonometric identities, we have
$sin(2\theta)=-1 \longrightarrow 2\theta=2k\pi+\frac{3\pi}{2} \longrightarrow \theta=k\pi+\frac{3\pi}{4}$.
Six examples $\theta=\frac{3\pi}{4}, \frac{7\pi}{4}, \frac{11\pi}{4}, \frac{15\pi}{4}, \frac{19\pi}{4}, \frac{23\pi}{4}$
