Answer
The two values of $\theta $ are $\frac{2\pi }{3}$ and $\frac{4\pi }{3}$.
Work Step by Step
We have the given expression: $\cos \theta =-\frac{1}{2}$.
Here, the reference angle is $\frac{\pi }{3}$ and $\theta $ lies in quadrants II or III.
Consider: The angle $\theta $ lies in quadrant II.
$\begin{align}
& \theta =\pi -\frac{\pi }{3} \\
& =\frac{3\pi -\pi }{3} \\
& =\frac{2\pi }{3}
\end{align}$
Consider: The angle $\theta $ lies in quadrant IV.
$\begin{align}
& \theta =\pi +\frac{\pi }{3} \\
& =\frac{3\pi +\pi }{3} \\
& =\frac{4\pi }{3}
\end{align}$
