\(=2\sqrt{3+\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}}\)
\(=2\sqrt{3+\sqrt{5-\left(2\sqrt{3}+1\right)}}\)
\(=2\sqrt{3+\sqrt{4-2\sqrt{3}}}\)
\(=2\sqrt{3+\sqrt{\left(\sqrt{3}-1\right)^2}}\)
\(=2\sqrt{3+\sqrt{3}-1}\)
\(=2\sqrt{2+\sqrt{3}}=\sqrt{8+4\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{6}+\sqrt{2}\right)^2}=\sqrt{6}+\sqrt{2}\)