Inverse trig functions!

Geometry Level 3

cot1(3)+cot1(7)+cot1(13)+cot1(21)+= ? \cot^{-1}(3) + \cot^{-1} (7) + \cot^{-1} (13) + \cot^{-1}(21) + \ldots = \ ?

Clarification: 3,7,13,21,3,7,13,21,\ldots is an increasing progression of integers for which the difference between the nn-th and (n1)(n-1)-th term is equals to 2n2n.

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