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

To prove that \( \cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma + \cos^2 \delta = \frac{4}{3} \), we will first define the angles and the diagonals of the cube.

### Step 1: Understanding the cube and its diagonals
A cube has vertices at the coordinates:
- \( A(0, 0, 0) \)
- \( B(a, 0, 0) \)
- \( C(a, a, 0) \)
- \( D(0, a, 0) \)
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