To simplify this expression, we first need to convert the angles into their equivalent values within the unit circle.

sin(π - π/3):
π - π/3 = 2π/3
sin(2π/3) = √3/2

cos(π + π/6):
π + π/6 = 7π/6
cos(7π/6) = -√3/2

tan(π/2 + π/3):
π/2 + π/3 = 5π/6
tan(5π/6) = -√3

Therefore, the expression simplifies to:
√3/2 -√3/2 -√3
= √3/2 √3/2 √3
= 3/4 * √3
= 3√3/4

So, sin(π - π/3) cos(π + π/6) tan(π/2 + π/3) simplifies to 3√3/4.