Revival Of This Problem. Part 1

Geometry Level 4

For the cube shown above, let

v=cos2w+cos2x+cos2y+cos2z.v = \cos^2 w + \cos^2 x + \cos^2 y + \cos^2 z.

If vv is in the form cd\frac{c}{d}, where cc and dd are coprime positive integers, find c+dc+d.

Note: ww, xx, yy and zz are all angles between 2 diagonals of the cube.


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