Prove a language is not recursive enumerable
Yes it's okay to use Rice's extended theorem.

To clarify, the theorem states: "if $C$ is some set of languages, and $C\neq\emptyset\wedge\Sigma^*\notin C$, then $\{&lt;M&gt;|L(M)\in C\}\notin RE$."

So, let us define $C=\{L((01)^*)\}$. Notice that our $L$ in the question is exaclty $\{&lt;M&gt;|L(M)\in C\}$, and then since $C\neq\emptyset$ and $\Sigma^*\notin C$ $[$as the only language in $C$ is $L((01)^*)\space]$, we have by the extended theorem that $L\notin RE$.