Question Number 32937 by abdo imad last updated on 06/Apr/18
$${let}\:{give}\:\mid{x}\mid<\mathrm{1}\:\:{prove}\:{that} \\ $$$$\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{sin}\left({n}\theta\right)}{{n}}\:{x}^{{n}} \:={arctan}\left(\:\frac{{xsin}\theta}{\mathrm{1}−{xcos}\theta}\right)\:. \\ $$