Question Number 130449 by Dwaipayan Shikari last updated on 25/Jan/21
$$\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }−\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }+\frac{\mathrm{1}}{\left(\mathrm{6}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }−\frac{\mathrm{1}}{\left(\mathrm{6}+\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }+\frac{\mathrm{1}}{\left(\mathrm{10}−\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }−\frac{\mathrm{1}}{\left(\mathrm{10}+\sqrt{\mathrm{3}}\right)^{\mathrm{3}} }+.. \\ $$