Evaluate the following integrals: \[ \int_{0}^{\pi / 2} \sqrt{\cos x-\cos ^{3} x}\left(\sec ^{2}...

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Evaluate the following integrals:
\[
\int_{0}^{\pi / 2} \sqrt{\cos x-\cos ^{3} x}\left(\sec ^{2} x-1\right) \cos ^{2} x d x
\]
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