Find the exact value of the real number $y$ if it exists. Do not use a calculator.
\[
y=\tan ^{-1} \frac{\sqrt{3}}{3}
\]
Select the correct choice and fill in any answer boxes in your choice below.
A.
\[
y=\tan ^{-1} \frac{\sqrt{3}}{3}=
\]
(Simplify your answer. Type an exact answer, using $\pi$ as needed. Use integers or fractions for any numbers in the expression.)
B.
\[
\tan ^{-1} \frac{\sqrt{3}}{3} \text { does not exist. }
\]

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: $y=\tan ^{-1} \frac{\sqrt{3}}{3} = \boxed{\frac{\pi}{6}}$