A line makes angles 60°,60°,45° and θ  with the four diagonals of a cube. Then sin2θ=

If a line makes angles  α,β,γ,δ with the four diagonals of a cube thencos2α+cos2β+cos2γ+cos2δ=43Here given  α=60°,β=60°,γ=45°and  δ=θHence,  cos260°+cos260°+cos245°+cos2δ=4314+14+12+cos2θ=43cos2θ=13Therefore,  sin2θ=1−13=23