sinA+sin(A+120°)+sin(A+240°)
=sinA+sin(A+120°)+sin(A+240°-360°)
=sinA+sin(A+120°)+sin(A-120°)
=sinA+sinAcos120°+cosAsin120°+sinAcos120°-cosAsin120°
=sinA+2sinAcos120°
=sinA-sinA
=0