I'm reading about equivalent definitions of Amenability of discrete groups in Brown&Ozawa.
In Theorem $2.6.8$ they list $10$ equivalent definitions. Two of them are: $6. \ C_r^*(G)=C^*(G)$ and $9. \ C_r^*(G)$ is nuclear.
There is a remark that nuclearity of $C_r^*(G)$ is equivalent to nuclearity of $C^*(G)$. One direction follows by $6.$. The other direcrion follows by The Trick, which is introduced in chapter $3$. I am familiar with The Trick and still can't see the converse direction.
Any help would be appreciated.