If , then find the value of…

MATHEMATICS · Subjective · AoPS · Mathematics · Sequences & Series · Sequences & Series

Problem

If ∑n=0∞2arccot⁡(n2+n+42)=kπ\sum_{n=0}^{\infty} 2 \operatorname{arccot}\left(\frac{n^2+n+4}{2}\right) = k\pi , then find the value of kk .

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