sinA+sinB+sinC
=2sin(A/2)cos(A/2)+2sin{(B+C)/2}cos{(B-C)/2}
=2cos(π/2-A/2)cos(A/2)+2cos(A/2)cos{(B-C)/2}
=2cos(A/2)*2cos{(π-A+B-C)/4}cos{(π-A-B+C)/2}
=4cos(A/2)cos(B/2)cos(C/2)

sinB+sinC-sinA
=2cos(A/2)*2sin{(π-A+B-C)/4}sin{(π-A-B+C)/2}
=4cos(A/2)sin(B/2)sin(C/2)

16cos^2(A/2)sin(B/2)cos(B/2)sin(C/2)cos(C/2)
=4cos^2(A/2)sinBsinC