$t(n) = \int_0^{\frac{\pi}{4}} \tan^{2n} x \, dx$
For $t(n)$ as defined above, $t(5) = \frac{a}{b} - \frac{\pi}{4}$, where $a$ and $b$ are coprime positive integers. Find $b - a$.
$t(n) = \int_0^{\frac{\pi}{4}} \tan^{2n} x \, dx$
For $t(n)$ as defined above, $t(5) = \frac{a}{b} - \frac{\pi}{4}$, where $a$ and $b$ are coprime positive integers. Find $b - a$.