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Is there any way how to avoid expressing $\zeta^{n-1}$ in terms of lower powers of $\zeta$ when working with cyclotomic fields?

K.<zeta> = CyclotomicField(3)
zeta^5
-zeta - 1

I would like to show $\zeta^2$ in this case.

I know that I can do this instead:

K.<zeta> = QQ[]
zeta^5 % (zeta^3 - 1)
zeta^2

But the problem is that eventually, I want to work with a polynomial ring over K and perform a factorization there, and that is not possible in QQ[].<x,y>.