Answer
$\theta=-\dfrac{\pi}{6}$ or, $-30^{\circ}$
Work Step by Step
We are given $\tan^{-1} (-\dfrac{\sqrt 3}{3})$
We know that the trigonometric function $\tan^{-1}$ has domain R and the range is: $[-\dfrac{\pi}{2}, \dfrac{\pi}{2}]$.
So, $\theta = \tan^{-1}(-\dfrac{\sqrt 3}{3})$
This implies that: $\theta=-\dfrac{\pi}{6}$ or, $-30^{\circ}$
