Find
\(\cos{x} =\)\( \sqrt{\cfrac{1+\sqrt{\cfrac{1+\sqrt{\cfrac{1-\sqrt{\cfrac{1+\cfrac{\sqrt{3}}{2}}{2}}}{2}}}{2}}}{2}}\)
in radians
my original answer was pi/96, I used the half-angle formula but it was marked incorrect, any ideas what I did wrong and how I can fix it?