To simplify the given expression:

sin(a - 2π/3) - sin(a + 2π/3)

Using the angle subtraction formula for sine, we have:

sin(x - y) = sin(x)cos(y) - cos(x)sin(y)

So, we apply this formula to the expression:

sin(a - 2π/3) - sin(a + 2π/3)
= sin(a)cos(2π/3) - cos(a)sin(2π/3) - (sin(a)cos(2π/3) + cos(a)sin(2π/3))
= sin(a)cos(2π/3) - cos(a)sin(2π/3) - sin(a)cos(2π/3) - cos(a)sin(2π/3)
= -2cos(a)sin(2π/3)
= -2cos(a)(sqrt(3)/2)
= -sqrt(3)cos(a)

Therefore, the simplified expression is:

-sqrt(3)cos(a)