To solve the equation sin(x/2 - π/3) - 1 = 0, we first need to isolate the sine term:

sin(x/2 - π/3) = 1

Now, recall that sin(π/3) = √3/2. Therefore, sin(π/3 - θ) = sin(θ).

Therefore, x/2 - π/3 = π/2

x/2 = π/2 + π/3

x/2 = 5π/6

x = 5π/3

So, the solution to the equation sin(x/2 - π/3) - 1 = 0 is x = 5π/3.