Starting with the operator 223z, draw up a tree diagram to show the evolution under first the 2-3 coupling, and then the 1-2 coupling. You do not need to work out all the sines and cosines to draw up the diagram, but just need to 'split1 each operator into the appropriate pair which arise from evolution of the coupling.
By inspecting your tree diagram, write down the trigonometric factors which multiply the operator 41z2z3z.