Prove that: \[ \cot ^{2} \theta\left(\frac{\sec \theta-1}{1+\sin \t...

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Prove that:
\[
\cot ^{2} \theta\left(\frac{\sec \theta-1}{1+\sin \theta}\right)+\sec ^{2} \theta\left(\frac{\sin \theta-1}{1+\sec \theta}\right)=0 .
\]
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