\(A=\sqrt{3-\sqrt{5-2\sqrt{3}}}-\sqrt{3+\sqrt{5+2\sqrt{3}}}\)
\(A^2=\left(\sqrt{3-\sqrt{5-2\sqrt{3}}}-\sqrt{3+\sqrt{5+2\sqrt{3}}}\right)^2\)
\(A^2=\left(3-\sqrt{5-2\sqrt{3}}\right)-2\sqrt{\left(3-\sqrt{5-2\sqrt{3}}\right)\left(3+\sqrt{5+2\sqrt{3}}\right)}+\left(3+\sqrt{5+2\sqrt{3}}\right)\)
\(A^2=\left(3-\sqrt{5-2\sqrt{3}}\right)-2\sqrt{9+3\sqrt{5+2\sqrt{3}}-3\sqrt{5-2\sqrt{3}}-\sqrt{\left(5-2\sqrt{3}\right)\left(5+2\sqrt{3}\right)}}+\left(3+\sqrt{5+2\sqrt{3}}\right)\)