Question: Find the value of tan-1 (tan 2π/3).
Solution:
We know that,
tan-1 tan x = x, x ∈ (-π/2, π/2)
$\tan ^{-1}\left(\tan \frac{2 \pi}{3}\right)=\tan ^{-1} \tan \left(\pi-\frac{\pi}{3}\right)=\tan ^{-1}\left(\tan \left(-\frac{\pi}{3}\right)\right)=-\frac{\pi}{3}$
