Question Number 136104 by Dwaipayan Shikari last updated on 18/Mar/21
$$\frac{{cos}\left(\mathrm{1}+\sqrt{\frac{\mathrm{43}}{\mathrm{3}}}\right)\pi}{\mathrm{1}^{\mathrm{2}} }+\frac{{cos}\left(\mathrm{1}+\sqrt{\frac{\mathrm{43}}{\mathrm{3}}}\right)\mathrm{2}\pi}{\mathrm{2}^{\mathrm{2}} }+\frac{{cos}\left(\mathrm{1}+\sqrt{\frac{\mathrm{43}}{\mathrm{3}}}\right)\mathrm{3}\pi}{\mathrm{3}^{\mathrm{2}} }+…={a}\pi \\ $$$${Find}\:{a} \\ $$