Answer
$-\dfrac{\pi}{6}$
Work Step by Step
Suppose $\theta =\tan (-\dfrac{\pi}{6})$
This gives: $\tan^{-1} \theta=\tan^{-1}[\tan(-\dfrac{\pi}{6})]$
The inverse property states that $\tan^{-1}(\tan a)=a $ satisfies for every $ a $ in the range $[-\dfrac{\pi}{2},\dfrac{\pi}{2}]$ .
Therefore, we have $\tan^{-1}[\tan(-\dfrac{\pi}{6})]=-\dfrac{\pi}{6}$
