Question Number 15578 by Joel577 last updated on 12/Jun/17
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\mathrm{cot}^{\mathrm{2}} \:\left(\frac{\pi}{\mathrm{14}}\right)\:+\:\mathrm{cot}^{\mathrm{2}} \:\left(\frac{\mathrm{3}\pi}{\mathrm{14}}\right)\:+\:\mathrm{cot}^{\mathrm{2}} \:\left(\frac{\mathrm{5}\pi}{\mathrm{14}}\right)\:? \\ $$