Summation of the Inverted Tangents

Geometry Level 2

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

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