Given that $μ$ and $Q$ are real constants and $i$ is a positive integer, evaluate
$$\sum_{i=1}^{+\infty}\;i\,\tan^{-1}\left(\frac{\mu Q}{\mu^2+\left(i^2-\frac{1}{4}\right)Q^2}\right)$$
Given that $μ$ and $Q$ are real constants and $i$ is a positive integer, evaluate
$$\sum_{i=1}^{+\infty}\;i\,\tan^{-1}\left(\frac{\mu Q}{\mu^2+\left(i^2-\frac{1}{4}\right)Q^2}\right)$$