Summation of the Inverted Tangents

Geometry Level 4

m=1[tan1(3m23m+1m63m5+3m4m3+1)]= ?\large \sum_{m=1}^{\infty} \left [ \tan^{-1} \left (\frac{3m^2-3m+1}{m^6-3m^5+3m^4-m^3+1} \right ) \right ] = \ ?

This is one of my original problems belonging to the set- Questions I've Made ©. Also try its sister problem

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