Chapter 7.3, Problem 65E

A tangent reduction formula Prove that for positive integers n ≠ 1,

${\displaystyle \int {\tan }^{n}xdx=\frac{{\tan }^{n-1}x}{n-1}-{\displaystyle \int {\tan }^{n-2}xdx.}}$

Use the formula to evaluate ${\displaystyle {\int }_0^{\pi /4}{\tan }^{3}xdx}$.