Working in the coordinate system where θ θ ^ ^ = z ^ ^ , we would like to show that S x and S y are rotated into each other by the angle θ. Starting with S x. Using units where ħ = 1 : S x → → U † † S x U = e i θ θ S z S x e − − i θ θ S z = S x + ( i θ θ ) [ S z , S x ] + ( 1 2 ! ) ( i θ θ ) 2 [ S z , [ S z , S x ] ] + ( 1 3 ! ) ( i θ θ ) 3 [ S z , [ S z , [ S z , S x ] ] ] + ⋯ ⋯