Explanation
Given,tan−1(12tan2A)+tan−1(cotA)+tan−1(cot3A)
=tan−1(tanA1−tan2A)+tan−1(cotA+cot3A1−cot4A)
=tan−1(tanA1−tan2A)+tan−1(cotA1−cot2A)
=tan−1(tanA1−tan2A)+tan−1(tanAtan2−1)
=tan−1(tanA1−tan2A)−tan−1(tanA1−tan2A)
=0
=π
=4(π4)
=4tan−1(1)
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