Answer
The two values of $\theta $ is $\frac{5\pi }{6}$ and $\frac{11\pi }{6}$.
Work Step by Step
The expression is $\tan \theta =\frac{-\sqrt{3}}{3}$.
Here, the reference angle is $\frac{\pi }{6}$ and $\theta $ lies in quadrants II or IV.
Consider: The angle $\theta $ lies in quadrant II.
$\begin{align}
& \theta =\pi -\frac{\pi }{6} \\
& =\frac{6\pi -\pi }{3} \\
& =\frac{5\pi }{3}
\end{align}$
Consider: The angle $\theta $ lies in quadrant IV.
$\begin{align}
& \theta =2\pi -\frac{\pi }{6} \\
& =\frac{12\pi -\pi }{6} \\
& =\frac{11\pi }{6}
\end{align}$
