The value of x that satisfies tan^-1(tan 3)=tan^2x, is

We have,

$tan^{-1}(tan 3) = tan^{-1}\begin{Bmatrix}tan (3 - \pi )\end{Bmatrix}=  3 - \pi < 0$

and, $tan^2 x ≥ 0$

$∴ tan^{-1}(tan 3) = tan^2 x $ has no solution.