Answer
$-\dfrac{\pi}{4}$
Work Step by Step
Suppose $\theta =\tan (-\dfrac{\pi}{3})$
This gives: $\tan^{-1} \theta=\tan^{-1}[\tan(-\dfrac{\pi}{3})]$
The inverse property states that $\tan^{-1}(\tan a)=a $ satisfies for every $ a $ in the range $(-\dfrac{\pi}{2},\dfrac{\pi}{2})$ . But the value $ a=\dfrac{3 \pi}{4}$ does not lie in the range of $(-\dfrac{\pi}{2},\dfrac{\pi}{2})$.
Therefore, we have $\tan^{-1}[\tan(\dfrac{3\pi}{4})]=-\dfrac{\pi}{4}$
