Finding maximum of this function in complex analysis

This particular question is from my assignment in complex analysis and I need to verify my answer and way of solving.

Let $f$ be analytic for $|z| leq 3$ such that $|f(z)| leq 1$ for $|z| leq 3$ and has $n$ roots at $w_{k}=e^{2 k pi i / 3}(k=0,1,2, ldots, n-1),$ the $n$ th roots of unity. What is the maximum value of $|f(0)| ?$ Which functions attain a maximum?

Attempt: Instead of using maximum modulus principle, I wrote the function as f(z) = $(z-w_1)… (z-w_k) $ and then putting z=0. $ |f(0)|= e^{ frac{2k(2k-1) πi} {3}} $ . But here maximum will depend upon value of k. So, how to find maximum?

Also, I don’t understand what it means by which functions attain it’s maximum.

If there is another method by which it can be solved more elegantly, please tell it.