If tan–1x + tan–1y = (4pi)/5, then cot–1x + cot–1y equals ______.

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If tan–1x + tan–1y = (4pi)/5, then cot–1x + cot–1y equals pi/5. Explanation: We have, tan–1x + tan–1y = (4pi)/5 $\Rightarrow$ `pi/2 - cot^-1x + pi/2 - cot^-1y = (4pi)/5 $\Rightarrow$ pi- (cot^-1x + cot^-1y) = (4pi)/5 .....(because tan^-1x + cot^-1x = pi/2) $\Rightarrow$ cot^-1x + cot^-1y = pi - (4pi)/5 $\Rightarrow$ cot^-1x + cot^-1y = pi/5`

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