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Let m = (tan-1 1 + tan-1 2 + tan-1 3)/(cot-1 1 + cot-1 2 + cot-1 3), then prove that (m + 2)m + 1 = 64.

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Given,m = (tan-1 1 + tan-1 2 + tan-1 3)/(cot-1 1 + cot-1 2 + cot-1 3)

π/(π/2) = 2

Hence, the value of

(m + 2)m + 1 = (2 + 2)3 = 43 = 64

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