Integrate with sin cos

Calculus Level 5

0π4(cos2θ)32cosθdθ\large\displaystyle \int_{0}^{\frac{\pi}{4}} (\cos 2 \theta)^{\frac{3}{2}} \cos \theta \, d \theta

Given the integral above equals to ABCπ \dfrac{A}{B \sqrt{C}} \pi where A,B,CA,B,C are positive integers with A,BA,B are coprime and CC square-free. Find BACB-A-C.

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