A line makes angles `angle, beta, gamma and delta` with the diagonals of a cube. Show that `cos^(2)alpha+cos^(2)beta+cos^(2)gamma+cos^(2)delta=4//3`.

Explanation

The direction ratios of the diagnols are

`1,1,1`

`-1,1,1`

`1,1,-1`

`-1,1,-1`

Hence, the let the direction fo the line be `1,a,b`

Now, the angle are

`cosalpha=(1+a+b)/sqrt3`

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