tan(3x/2)-tan(x/2)-2sinx/(cosx+cos2x)
=sin(3x/2)/cos(3x/2)-sin(x/2)/cos(x/2)-2sinx/(cosx+cos2x)
=[sin(3x/2)cos(x/2)-cos(3x/2)sin(x/2)]/cos(3x/2)cos(x/2)-2sinx/(cosx+cos2x)
=2sin(3x/2-x/2)/[cos(3x/2+x/2)+cos(3x/2-x/2)]-2sinx/(cosx+cos2x)
=2sinx/(cos2x+cosx)-2sinx/[cosx+cos(2x)]
=0