JEE Advanced Indefinite Integration 2

Calculus Level 5

If I=dxsinxsin(2x+α)\displaystyle I=\int \dfrac{dx}{\sin x \sqrt{\sin (2x+\alpha)}} for 0<α<π20<\alpha<\dfrac{\pi}{2} and f(x)=logcotx+cotα+cot2xcsc2αf(x)=\log \left |\cot x+\cot \alpha + \sqrt{\cot^2x-\csc^2\alpha }\right |, then find II.

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