Clearly $334 = 2 \times 167$. So it is of the form $2p^k$ which implies primitive roots $\bmod 334$ exits but the question is how many?
The formula $\phi(\phi(n))$ requires $n$ to be prime. If we use it for $334$ which is composite, we get $\phi(\phi(334)) = 82$.
So can we conclude that there are $82$ primitive roots $\bmod 334$?