Geometry Level 4

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

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

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