JEE Advanced Indefinite Integration 2

Calculus Level 5

If \(\displaystyle I=\int \dfrac{dx}{\sin x \sqrt{\sin (2x+\alpha)}}\ (0<\alpha<\dfrac{\pi}{2})\), \(f(x)=\log \left |\cot x+\cot \alpha + \sqrt{\cot^2x-\csc^2\alpha }\right |\), then \(I\) equals

This problem is a part of My picks for JEE Advanced 1
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