To solve this equation, we will simplify each trigonometric term:

sin(π-x) = sin(π)cos(x) - cos(π)sin(x) = 0 - (-1)sin(x) = sin(x)cos(π/2-x) = cos(π/2)cos(x) + sin(π/2)sin(x) = 0 + 1*sin(x) = sin(x)

Now we can rewrite the equation as:
sin(x) + sin(x) - sin(x) = -1
2sin(x) = -1
sin(x) = -1/2

So, x = π/6 + 2πn or x = 5π/6 + 2πn, where n is an integer.