`Clear[t, r, z] c = 1; gam = 1.; tm = 16.; r[t_] = 2 c ArcTanh[Tan[t/(2 Sqrt[1 - Cot[gam]^2])]]; z[t_] = r[t] Cot[gam]; plr = PolarPlot[r[t], {t, 0, tm}, GridLines -> Automatic, PlotStyle -> {Blue, Thick}] rad = Plot[r[t], {t, 0, tm}, GridLines -> Automatic, PlotStyle -> {Red, Thick}] pp3 = ParametricPlot3D[{r[t] Cos[t], z[t], r[t] Sin[t]}, {t, -tm, tm}, PlotStyle -> {Magenta, Thick}] FindRoot[r[t] = 1.25, {t, 1.2345}] `

The last line `FindRoot`

does not work due to Jacobian singularity. Can there be some work around? Thanks for help.