3d Geometry: A line makes angles alpha, beta, gamma and delta with four diagonals of a cube.

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Prove that cos²α + cos²β + cos²γ + cos²δ = 4/3. A line makes α,β,γ,δ with four diagonals of cube... Prove that cos²α + cos²β + cos²γ + cos²δ = 4/3. A line makes α,β,γ,δ with four diagonals of cube...