What is$\sum_{n=1}^\infty\frac{1}{n^2+1}$?

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What is $$\sum_{n=1}^\infty\frac{1}{n^2+1}$$ I know that $\sum_{n=1}^\infty\frac1{n^2}=\frac{\pi^2}6$ but what about if we add a one to it in the denominator, can we still figure it out?