Inverse trig functions!

Geometry Level 3

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

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

0

\frac { \pi }{ 3 }

\frac { \pi }{ 4 }

1

\frac { \pi }{ 2 }

{ \pi }