Summation of the Inverted Tangents

Geometry Level 3

Evaluate m=1tan1(8m16m432m2+5).\large \sum_{m=1}^{\infty} \tan^{-1} \left(\frac{8m}{16m^4-32m^2+5}\right).

Remember that the range of the inverse tangent function is (π2,π2) ( - \frac{ \pi}{2} , \frac{ \pi }{2}) .

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