Question Number 95598 by bagjamath last updated on 26/May/20
$$\mathrm{If}\:\:\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{1}} +\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}} +…+\mathrm{sin}^{−\mathrm{1}} {x}_{\mathrm{2}{n}} ={n}\pi, \\ $$$$\mathrm{then}\:\:\:\underset{\underset{{i}\:\neq\:{j}} {{i},\:{j}=\mathrm{1}}} {\overset{\mathrm{2}{n}} {\sum}}\:\:\:{x}_{{i}} \:{x}_{{j}} \:= \\ $$