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 \(2n\).

\[\frac { \pi }{ 3 } \] \[0\] \[{ \pi } \] \[\frac { \pi }{ 4 } \] \[\frac { \pi }{ 2 } \] \[1\]

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