Running `nano` uses the old nano(2.0.6) even though nano 3.0 is installed I installed nano 3.0 with brew install nano, but when I run nano --version, it shows version 2.0.6, which is what came with macOS.

Screenshot:


echo $PATH also shows that /usr/local/bin is listed before /usr/bin

How do I make running nano use version 3.0 and not 2.0.6?

This doesn't help as nano is already in /usr/local/bin and /usr/local/bin is listed first in $PATH and /etc/paths.
You don't make nano "use" anything. You run the executable you want, from the shell. Bash keeps a hash of where binaries are. If you type type nano, and it shows you the system-provided one, restart your shell or use the command hash -r to force the shell to re-hash the paths. Also, cat /etc/paths is meaningless, instead echo $PATH.