Integrate challenge 1

Calculus Level 5

\[\large{\displaystyle \int^{1}_{0} \frac{\sin x(\cos^2 x-\cos^2 \frac{\pi}{5} )(\cos^2 x-\cos^2 \frac{2\pi}{5} )}{\sin 5x}.dx}\]

The value of above integral is \(\large{\frac{a}{b}}\). Find \(a+b\).

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