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$\pi /3$cos$x$ + sin$\pi /3$sin$x$ = 0

Since cos$\pi /3$ = 1/2 and sin$\pi /3$ = √3/2, we get:

$1/2$cos$x$ + $\surd 3/2$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$-\surd 3$. Solving this in a calculator we get x ≈ -1.047 $inradians$.