Look at that exponent

Calculus Level 3

\[\large \int_{0}^{\frac{\pi}{2}} \dfrac{1}{1+\tan^{\frac{4}{25}}(x)} \mathrm{d}x\]

If the above integral evaluates to a number that can be written in the form \(\dfrac{a\pi}{b}\), where \(a\) and \(b\) are coprime, positive integers, find \(a+b\).

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