Does Machin-like formula help?

Geometry Level 3

\[ \tan^{-1} \left ( \frac 13 \right) + \tan^{-1} \left ( \frac 17 \right)+ \tan^{-1} \left ( \frac 1{13} \right)+ \tan^{-1} \left ( \frac 1{21} \right)+ \ldots = \ ? \]

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