$\sqrt{1+\sqrt{1-4x^{2}}}=x\left ( 1+\sqrt{1+\sqrt{1+2\sqrt{1-4x^{2}}}}\right )$
$\sqrt{1+\sqrt{1-x^{2}}}\left ( \sqrt{\left ( 1+x \right )^{3}}-\sqrt{\left ( 1-x \right )^{3}} \right )=\frac{2}{\sqrt{3}}+\sqrt{\frac{1-x^{2}}{3}}$
$\left ( 64x^{3}-112x^{2}+56x-7 \right )^{2}=4-4x$