To solve this equation, we first need to isolate the cosine function.

Firstly, rewrite the equation in terms of cosine:
cos(x/3 + π/6) = 2/9

Next, take the inverse cosine of both sides to remove the cosine function:
x/3 + π/6 = arccos(2/9)

Now, we need to solve for x:
x/3 = arccos(2/9) - π/6

Multiply both sides by 3 to isolate x:
x = 3(arccos(2/9) - π/6)

Therefore, the solution to the equation is x = 3(arccos(2/9) - π/6).