To find the value of x, we can use the trigonometric identity:

sin(pi + x) = sin(pi)cos(x) + cos(pi)sin(x)

Since sin(pi) = 0 and cos(pi) = -1, we have:

sin(pi + x) = 0cos(x) + (-1)sin(x)
sin(pi + x) = -sin(x)

Now, we need to find where cos(-pi/3) = -sin(x). We know that cos(-pi/3) = cos(pi/3), so we have:

cos(pi/3) = -sin(x)
cos(60 degrees) = -sin(x)
1/2 = -sin(x)

Since sin(30 degrees) = 1/2, we have x = -30 degrees (or -pi/6 in radians).