For the cube shown above, let

\[v = \cos^2 w + \cos^2 x + \cos^2 y + \cos^2 z.\]

If \(v\) is in the form \(\frac{c}{d}\), where \(c\) and \(d\) are coprime positive integers, find \(c+d\).

**Note:** \(w\), \(x\), \(y\) and \(z\) are all angles between 2 diagonals of the cube.

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