Arctangent Summation

Geometry Level 4

n=1tan1(2nn4+n2+2)\large\displaystyle\sum_{n=1}^{\infty}\tan^{-1}\left(\dfrac{2n}{n^4+n^2+2}\right)

If the value of the summation above is in the form of abπ\dfrac ab\pi, where aa and bb are coprime positive integers, find a+ba+b.

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