Answer
$\frac{\pi}{6}$
Work Step by Step
We need to find the angle between $-\frac{\pi}{2}$ and $\frac{\pi}{2}$. The tangent is $\frac{\sqrt 3}{3}$.
$\frac{\sqrt 3}{3}=\frac{1}{\sqrt 3}=\frac{\frac{1}{2}}{\frac{\sqrt 3}{2}}=\frac{\sin\frac{\pi}{6}}{\cos\frac{\pi}{6}}=\tan\frac{\pi}{6}$
The angle is $\frac{\pi}{6}$.
$\arctan \frac{\sqrt 3}{3}=\frac{\pi}{6}$
