I find nettles far less resilient that you might imagine. I would expect a
good rotavate and rake to get rid of most of them without the need for
chemicals.

Of course chemicals will also help against the other weeds that might be
around. Depends on whether you want an organic garden, or not.

BTW, nettles are good activators in a compost heap as well as attracting
various insects so you might want to keep a patch around.

Paul DS.