Answer
The two values of $\theta $ are $\frac{5\pi }{4}$ and $\frac{7\pi }{4}$.
Work Step by Step
We have the given expression: $\sin \theta =-\frac{\sqrt{2}}{2}$.
Here, the reference angle is $\frac{\pi }{4}$ and $\theta $ lies in quadrants III or IV.
Consider: The angle $\theta $ lies in quadrant III.
$\begin{align}
& \theta =\pi +\frac{\pi }{4} \\
& =\frac{5\pi }{4}
\end{align}$
Consider: the angle $\theta $ lies in quadrant IV.
$\begin{align}
& \theta =2\pi -\frac{\pi }{4} \\
& =\frac{8\pi -\pi }{4} \\
& =\frac{7\pi }{4}
\end{align}$