Answer
The two values of $\theta $ are $\frac{\pi }{3}$ and $\frac{5\pi }{3}$.
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 I or IV.
Consider: the angle $\theta $ lies in quadrant I.
$\theta =\frac{\pi }{3}$
Or the angle $\theta $ lies in quadrant IV.
$\begin{align}
& \theta =2\pi -\frac{\pi }{3} \\
& =\frac{6\pi -\pi }{3} \\
& =\frac{5\pi }{3}
\end{align}$
