The value of \( \int_{0}^{1} \cos ^{-1}\left(\left(x-x^{2}\right)-\...

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The value of \( \int_{0}^{1} \cos ^{-1}\left(\left(x-x^{2}\right)-\sqrt{\left(1-x^{2}\right)\left(2 x-x^{2}\right)}\right) d x \) is
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