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