To solve for x, we can use the identity

cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

In this case, a = π/3 and b = x. According to the given formula:

cos(π/3)cos(x) + sin(π/3)sin(x) = 0

Since cos(π/3) = 1/2 and sin(π/3) = √3/2, we get:

(1/2)cos(x) + (√3/2)sin(x) = 0

Multiplying through by 2 to clear fractions gives:

cos(x) + √3sin(x) = 0

Dividing through by cos(x) gives:

tan(x) = -√3

This means that x = arctan(-√3). Solving this in a calculator we get x ≈ -1.047 (in radians).