Answer
$-\dfrac{ 3 \pi}{8}$
Work Step by Step
Value of certain composite functions formula:
$f^{-1}(f(x)= \tan^{-1}{(\tan{x})} = x \hspace{25pt} -\dfrac{\pi}{2}\leq x \leq \dfrac{\pi}{2}$
Therefore,
$\tan^{-1} {\left[\tan{\left(-\dfrac{ 3 \pi}{8} \right)} \right]} = -\dfrac{ 3 \pi}{8}$
