Step 1 :The question is asking for the value of $y$ where $y$ is the inverse tangent of $\frac{\sqrt{3}}{3}$. The inverse tangent function, also known as arctan, is the inverse of the tangent function. It returns the angle whose tangent is a given number.
Step 2 :The tangent of an angle in a right triangle is the ratio of the opposite side to the adjacent side. So, we need to find an angle whose tangent is $\frac{\sqrt{3}}{3}$.
Step 3 :We know that $\tan(\frac{\pi}{6}) = \frac{\sqrt{3}}{3}$, so $\tan^{-1}(\frac{\sqrt{3}}{3}) = \frac{\pi}{6}$.
Step 4 :Final Answer: $y=\tan ^{-1} \frac{\sqrt{3}}{3} = \boxed{\frac{\pi}{6}}$