Sin(π\3-a)-sin(π/3+a) ?

sin(π/3 + a) = sin(π/3)cosa + cos(π/3)sina
sin(π/3 - a) = sin(π/3)cosa - cos(π/3)sina
sin(π/3 - a) - sin(π/3 + a) = sin(π/3)cosa - cos(π/3)sina - sin(π/3)cosa - cos(π/3)sina =
= -2cos(π/3)sina = -2 * (1/2) sina = -sina