Diagonals of a cube

Geometry Level 4

A line makes angles \( \alpha , \beta , \gamma , \delta \) with the four diagonals of a cube.

If \( \cos^2{\alpha} + \cos^2{\beta} + \cos^2{\gamma} + \cos^2{\delta} \) can be written as \( \dfrac ab\), where \(a\) and \(b\) are coprime positive integers, find \(a+b\).

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