If \( \alpha \in\left(-\frac{3 \pi}{2},-\pi\right) \), then the value of \( \tan ^{-1}(\cot \alp...

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If \( \alpha \in\left(-\frac{3 \pi}{2},-\pi\right) \), then the value of \( \tan ^{-1}(\cot \alpha) \) \( -\cot ^{-1}(\tan \alpha)+\sin ^{-1}(\sin \alpha)+\cos ^{-1}(\cos \alpha) \) is equal to
(1) \( 2 \pi+\alpha \)
(2) \( \pi+\alpha \)
(3) 0
(4) \( \pi-\alpha \)
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