play with diagonals of cube

Geometry Level pending

A line makes angles \(\alpha ,\beta ,\gamma ,\delta\) with four diagonals of a cube . If the value of \(\sum _{ r\epsilon \left\{ \alpha ,\beta ,\gamma ,\delta \right\} }^{ }{ {\ cos }^{ 2 }r } \) is in the form of \(a/b\) .Find the value of a+b where a and b are integer ?

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