Arctangent Summation

Geometry Level 4

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

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

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