$I_n = \begin{align*} \int_0^{\pi/4} \tan^n x \; dx \end{align*}$ then $\displaystyle\lim_{n \to \infty} n [I_n + I_{n+2} ]$ equals :

Question

( A ) $\frac{1}{2}$
( B ) $zero$
( C ) $1$
( D ) $\infty$