If \( \tan ^{-1}\left(\sin ^{2} \theta+2 \sin \theta+2\right)+\cot ^{-1}\left(4 \sec ^{2} \phi+1...

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If \( \tan ^{-1}\left(\sin ^{2} \theta+2 \sin \theta+2\right)+\cot ^{-1}\left(4 \sec ^{2} \phi+1\right)=\frac{\pi}{2} \) has solution for some \( \theta \) and \( \phi \) then
(a) \( \sin \theta=-1 \)
(b) \( \sin \phi=1 \)
(c) \( \cos \theta=1 \)
(d) \( \cos \phi=-1 \)
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