Adding arctan

Geometry Level 4

n=0arctan(1n2+n+1) \large \sum_{n=0}^\infty \text{arctan} \left( \dfrac1{n^2+n+1} \right)

If the value of the summation above is in the form of daπy \dfrac da \pi ^y , where a,da,d and yy are positive integers with a,da,d coprime, find d+a+yd+a+y.

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