\sqrt{2+\sqrt3}*\sqrt{2+\sqrt{2+\sqrt3}}*\sqrt{2+\sqrt{2+\sqrt{2+\sqrt3}}}*\sqrt{2-\sqrt{2+\sqrt{2+\sqrt3}}}=
\sqrt{2+\sqrt3}*\sqrt{2+\sqrt{2+\sqrt3}}*\sqrt{(2+\sqrt{2+\sqrt{2+\sqrt3}})*(2-\sqrt{2+\sqrt{2+\sqrt3}})}=
=\sqrt{2+\sqrt3}*\sqrt{2+\sqrt{2+\sqrt3}}*\sqrt{4-2+\sqrt{2+\sqrt3}}=
=\sqrt{2+\sqrt3}*\sqrt{2+\sqrt{2+\sqrt3}}*\sqrt{2+\sqrt{2+\sqrt3}}=
=\sqrt{2+\sqrt3}*(\sqrt{2+\sqrt{2+\sqrt3}})^2=
=\sqrt{2+\sqrt3}*(2+\sqrt{2+\sqrt3})=
=2\sqrt{2+\sqrt3}+(\sqrt{2+\sqrt3})^2=
=2\sqrt{2+\sqrt3}+2+\sqrt3