Simplifying a product over roots of unity

Question

Let $\zeta_{n}=e^{2\pi i /n}$ be the nth root of unity. Now consider the product : $$\prod_{k=1}^{n-1} (1-\zeta_{n}^{k})^{\zeta_{n}^{k}}$$ Is there a simple formula for this product as a function of $n$ !?