$\sqrt{2+\sqrt{2}}.\sqrt{3+\sqrt{7+\sqrt{2}}}.\sqrt{3+\sqrt{6+\sqrt{7+\sqrt{2}}}}.\sqrt{3-\sqrt{6+\sqrt{7+\sqrt{2}}}}
\\=\sqrt{2+\sqrt{2}}.\sqrt{3+\sqrt{7+\sqrt{2}}}.\sqrt{9-(6+\sqrt{7+\sqrt{2}})}
\\=\sqrt{2+\sqrt{2}}.\sqrt{3+\sqrt{7+\sqrt{2}}}.\sqrt{3-\sqrt{7+\sqrt{2}}}
\\=\sqrt{2+\sqrt{2}}.\sqrt{9-(7+\sqrt{2})}
\\=\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2}}
\\=\sqrt{4-2}=\sqrt{2}$