Does this work for you?
julia> theta = nlsolve(x -> f_aux(max.(0.0, x)), x0).zero
1-element Vector{Float64}:
0.06408989836281948
Does this work for you?
julia> theta = nlsolve(x -> f_aux(max.(0.0, x)), x0).zero
1-element Vector{Float64}:
0.06408989836281948