Find the principal value of `tan^(-1)(-sqrt3).`

Explanation

Let `tan^(-1)(-sqrt3)=theta`.Then ,`tan theta=-sqrt3= -tan pi-3 =tan( - pi/3)`
We know that the range of the principal value branch of `tan^(-1) is (- pi/2, pi/2)` and `tan (- pi/3)= -sqrt3`.
Therefore, principal value of `tan^(-1)(-sqrt3)` is `- pi/3.`