play with diagonals of cube

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 ?