A line makes angles `alpha,""""beta,""""gamma` and `delta` with the diagonals of a cube, prove that `cos^2alpha+cos^2beta+cos^2gamma+cos^2delta=4/3`

Explanation

Let us start by taking 'O' as a corner


OA,OB,OC be the 3 edges through the axes


Let OA=OB=OC=a

coordinates of O=(o,o,o)

A(a,o,o)B(o,a,o)C(o,o,a)
P(a,a,o)L(o,a,a)M(a,o,a)N(a,a,o)

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