Question Number 113793 by Eric002 last updated on 15/Sep/20
$${prove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{sin}^{\mathrm{2}} \left(\pi{k}\right)−\pi{k}\:{sin}\left({kx}\right)\:{cos}\left(\pi{k}\right)}{{k}^{\mathrm{2}} }=\frac{\pi}{\mathrm{4}} \\ $$