A thin rod is initially coincident with the Z axis when it is given three rotations defined by the Euler angles ϕ = 30°, θ = 45°, and ψ = 60°. If these rotations are given in the order stated, determine the coordinate direction angles α, β, γ of the axis of the rod with respect to the X, Y, and Z axes. Are these directions the same for any order of the rotations? Why?