How to calculate the following: $\sum_{n=0}^\infty \frac{1}{1+n^2}=\;\;?$

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How can I calculate the following sum?

any hint please? I am beginner in such things, i have tried to make a decomposition for the denominator but no result $$\sum_{n=0}^\infty \frac{1}{1+n^2}=?$$