How to simplify summation containing trignometric function?

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Prove that $$2 \sum\limits_{n=1}^\infty \left(\frac{x}{b}\right)^n \frac{\sin A}{n} = \tan^{-1}\left(\frac{2bx \cos A}{b^2-x^2}\right)$$

I have tried to do by changing this into imaginary part of exponential function but can't proceed more..