sinA+sin(120°+A)+sin(240°+A)=sinA+sin(180°-60°+A)+sin(180°+60°+A)=sinA+sin(60°-A)-sin(60°+A)=sinA+sin60°cosA-cos60°sinA-(sin60°cosA+cos60°sinA)=sinA-2cos60°sinA=sinA-sinA=0