sinx+sin(x+2π/3)+sin(x+4π/3)
=sinx+(x + π - π/3)+sin(x + π + π/3)
=sinx+sin[π-(π/3-x)]+sin[π+(π/3+x)]
=sinx+sin(π/3-x)-sin(π/3+x)
=sinx-[sin(π/3+x)-sin(π/3-x)]
=sinx-2cos(π/3)sinx
=sinx-sinx
=0