To solve the equation sin(2π + x) - cos(3π/2 - x) = √3, we can use trigonometric identities and properties.

First, let's expand sin(2π + x) and cos(3π/2 - x) using angle addition formulas:
sin(2π + x) = sin(2π)cos(x) + cos(2π)sin(x) = 0cos(x) + (-1)sin(x) = -sin(x)
cos(3π/2 - x) = cos(3π/2)cos(x) + sin(3π/2)sin(x) = 0cos(x) + (-1)sin(x) = -sin(x)

Now, substitute these values back into the equation:
-sin(x) - (-sin(x)) = √3
-sin(x) + sin(x) = √3
0 = √3

Since 0 is not equal to √3, there seems to be a mistake in the equation or the calculations. The equation sin(2π + x) - cos(3π/2 - x) = √3 may not have a valid solution.