Верно ли равенство?Нужно полное решение

$\sqrt{2 + \sqrt{12 + 4\sqrt{13+4\sqrt{3}}}} =\sqrt{2 + \sqrt{12 + 4\sqrt{1 + 2*1*2\sqrt{3} + 12}}} = \\\\ =\sqrt{2 + \sqrt{12 + 4\sqrt{1^2 + 2*1*2\sqrt{3} + (2\sqrt{3})^2}}} =\\\\ =\sqrt{2 + \sqrt{12 + 4\sqrt{(1+2\sqrt{3})^2}}} =\\\\$

$=\sqrt{2 + \sqrt{12 + 4(1+2\sqrt{3})}} = \sqrt{2 + \sqrt{16 + 8\sqrt{3}}} =\\\\ = \sqrt{2 + \sqrt{4 + 2*2*2\sqrt{3} + 12}} = \sqrt{2 + \sqrt{2^2 + 2*2*2\sqrt{3} + (2\sqrt{3})^2}} =\\\\ = \sqrt{2 + \sqrt{(2+2\sqrt{3})^2}} =\sqrt{4 +2\sqrt{3}} = \sqrt{1^2 +2\sqrt{3} + 3^2} =\\\\ =\sqrt{1^2 +2*1*\sqrt{3} + (\sqrt{3})^2} = \sqrt{(1 + \sqrt{3})^2} = 1 + \sqrt{3}$

Равенство верное.