Find the right signs

[George Plousos]

Find the right signs to make the following equality true.

[tex]\sqrt{2 - \sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \sqrt{2 \pm \sqrt{2}}}}}}}}[/tex]

[tex]= 2 \sin \left (90^{\circ} (2 \times 57 + 1)/2^8 \right )[/tex]

Hint: The solution is related to the Gray code of [tex]57[/tex]. This applies to any other integer k with [tex]32 \leq k \leq 63[/tex] that will be placed in place of [tex]57[/tex].