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\[\large{\displaystyle \int^{\pi}_{0} \frac{\sin^4 x \sqrt{(1-\cos x)}}{(1+\cos x)^2} dx=\frac{A\sqrt{B}}{C}}\]

where \(A,C\) are co prime integers and \(B\) is square free

Find \(A+B+C\)

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