Replace Greek symbols with A, B, C.
sin(A+B+C)=sinAcos(B+C)+cosAsin(B+C)=
sinA(cosBcosC-sinBsinC)+cosA(sinBcosC+cosBsinC)=
sinAcosBcosC-sinAsinBsinC+cosAsinBcosC+cosAcosBsinC.
This is the same as sinAcosBcosC+cosAsinBcosC+cosAcosBsinC-sinAsinBsinC.
Replace A, B, C with original Greek symbols.