Chapter 5.7, Problem 109E

To determine

To evaluate:

$I={\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{d\theta }{1+{\tan }^{6000}\theta }}$ by using substitution show that I is equals to $J={\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{d\theta }{1+{\cot }^{6000}\theta }}$ and show that $I+J={\displaystyle \underset{0}{\overset{\frac{\pi }{2}}{\int }}d\theta }$