Evaluate $\sum_{n=0}^{\infty} \operatorname{Arccot}\left(n^2+n+1\right)$, where $\operatorname{Arccot} t$ for $t \geqslant 0$ denotes the number $\theta$ in the interval $0<\theta \leqslant \pi / 2$ with $\cot \theta=t$. The original answer is in the format \frac{m\pi}{n}, please give the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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