Non-Linear Optimization - Query

You can also try my package "nleqslv" for solving systems of non linear
equations (using Broyden or Newton with a selection of global strategies).

library(nleqslv)

xinit <- rep(1,3) ? ? ? ? ? ? ? # or rep(0,3) for a singular start
nleqslv(xinit,f2,control=list(trace=1)) ?# f2 defined as above

(You don't need the trace=1; but especially when doing first explorations of
a system it can come in handy).