Problem Analysis #5

Return a single integer only. The problem has been revised so that no final answer is an irrational number, a parameterized expression, a range, a proof, a drawing, a graph, a locus equation, or a region description.

For

let $\alpha$ be the number satisfying $0<\alpha<\pi/4$ and $f'(\tan\alpha)=0$. Let $u=\tan\alpha$. The value of $u$ is irrational, so instead compute the integer