To solve the equation cos(x + π/3) = -1 in the interval [-2π, π/2], we first need to find the values of x that satisfy this equation.

Since the cosine function has a period of 2π, we can simplify the interval to just [0, 2π]. The general solution for cos(x) = -1 is x = π + 2πn, where n is an integer.

Now, we need to consider the angle inside the cosine function: (x + π/3). When the cosine of an angle is -1, the angle must be π, so we have:

x + π/3 = π

Solving for x, we get:
x = π - π/3
x = 2π/3

Since 2π/3 is between 0 and 2π, it satisfies the given interval.

Therefore, the solution to the equation cos(x + π/3) = -1 in the interval [-2π, π/2] is:
x = 2π/3