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

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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