Inverse summation!

Geometry Level 3

tan1(22+12+14)+tan1(42+22+24)+tan1(62+32+34)+= ? \begin{aligned} && \tan^{-1} \left(\frac2{2+1^2+1^4}\right) \\ &+& \tan^{-1} \left(\frac4{2+2^2+2^4}\right) \\ &+& \tan^{-1} \left(\frac6{2+3^2+3^4}\right) \\ &+& \ldots = \ ? \end{aligned}

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