Let \(x^3 - x + 1 \in \mathbb{Z}_3[x]\), where \(\mathbb{Z}_3[x]\) is the ring of all polynomials with coefficients in \(\mathbb{Z}_3\). Then the degree of the field extension
\[
\left. \mathbb{Z}_3[x] \middle/ \langle x^3 - x + 1 \rangle \right.
\]
of \(\mathbb{Z}_3\) is equal to ______. (answer in integer)