Prove that \( \mathrm{P} \) \[ \int_{0}^{\pi / 2} \frac{\sin ^{7} x...

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Prove that
\( \mathrm{P} \)
\[
\int_{0}^{\pi / 2} \frac{\sin ^{7} x}{\left(\sin ^{7} x+\cos ^{7} x\right)} d x=\frac{\pi}{4}
\]
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