sin(π/6 - t) - cos(π/3 + t)

sin(π/6)cos(t) - cos(π/3)sin(t) - sin(π/3)cos(t) - cos(π/3)sin(t)

(1/2)(cos(t)) - (sqrt(3)/2)(sin(t)) - (sqrt(3)/2)(cos(t)) - (1/2)(sin(t))

(1/2 - sqrt(3)/2)cos(t) - (sqrt(3)/2 + 1/2)sin(t)

(cos(π/6) - sin(π/6))cos(t) - (sin(π/6) + cos(π/6))sin(t)

cos(π/6 + t) - sin(π/6 + t)

sin(t + π/6) - cos(t + π/6)

Therefore, the simplified expression is sin(t + π/6) - cos(t + π/6).