Answer
$\frac{5\pi}{4}+2k\pi$ and $\frac{7\pi}{4}+2k\pi$
Work Step by Step
Given $sin\theta=-\frac{\sqrt 2}{2}$, we can find two values in $[0,2\pi]$ $\theta=\frac{5\pi}{4}, \frac{7\pi}{4}, $
and the general solutions are $\theta=\frac{5\pi}{4}+2k\pi$ and $\theta=\frac{7\pi}{4}+2k\pi$ where $k$ is any integer.
