Given a birational proper morphism $f\colon X \rightarrow Y$ of complex algebraic varieties. It is always true that $f^* \colon \pi^{et}_1 (X)\rightarrow \pi^{et}_1(Y)$ is an isomorphism? I think that this follows from (SGA.1 exp X. Corollary 1.4) But im not totally sure.
Thanks, in advance.