Inspired by my Best Friend

Geometry Level 4

\[\Large \cot ^{-1} 2 + \cot ^{-1} 8 + \cot ^{-1} 18 + \ldots = \ ? \]

Give your answer to 3 decimal places in radians.

Clarification: \(2,8,18,\ldots\) are twice a perfect square.


This is not my original problem.
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