\(\sqrt{2+\sqrt{3}} \times \sqrt{2+\sqrt{2+\sqrt{3}}} \times \sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}} \times \sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\) is equal to

Let a = sqrt(2+sqrt(2+sqrt3)). Last two factors: sqrt(4-a^2) = sqrt(2-sqrt(2+sqrt3)); times second factor gives sqrt(4-(2+sqrt3)) = sqrt(2-sqrt3); times first factor gives sqrt(4-3) = 1.