Extract data from a Parametric2D plot

I'm trying to extract the data from a parametric plot via the following:

Subscript[\[Epsilon], e] = 0.0005;
Subscript[R, 0] = 15;
f[\[Theta]_, \[Phi]_] :=
1 + (4 Subscript[\[Epsilon], e])/(1 -
3 Subscript[\[Epsilon], e]) (Cos[\[Theta]]^4 +
Sin[\[Theta]]^4 (1 - 2 Sin[\[Phi]]^2 Cos[\[Phi]]^2));
x = Subscript[R,
0] (f[\[Theta], \[Phi]] Sin[\[Theta]] Cos[\[Phi]] +
D[f[\[Theta], \[Phi]], \[Theta]] Cos[\[Theta]] Cos[\[Phi]] - (D[
f[\[Theta], \[Phi]], \[Phi]] Sin[\[Phi]])/Sin[\[Theta]]);
y = Subscript[R,
0] (f[\[Theta], \[Phi]] Sin[\[Theta]] Sin[\[Phi]] +
D[f[\[Theta], \[Phi]], \[Theta]] Cos[\[Theta]] Sin[\[Phi]] + (D[
f[\[Theta], \[Phi]], \[Phi]] Cos[\[Phi]])/Sin[\[Theta]]);
z = Subscript[R,
0] (f[\[Theta], \[Phi]] Cos[\[Theta]] -
D[f[\[Theta], \[Phi]], \[Theta]] Sin[\[Theta]]);

Now, Parametric2D gives me the desired figure.

ParametricPlot[{x, y}, {\[Theta], 0, 2 \[Pi]}, {\[Phi], 0,
2 \[Pi]}, PlotStyle -> None, MeshFunctions -> {#3 &},
Mesh -> {{{\[Pi]/2, Directive[Opacity, Blue, Thick]}}}]

Next I need to save the data, and I do the following

data = Cases[
ParametricPlot[{x, y}, {\[Theta], 0, 2 \[Pi]}, {\[Phi], 0,
2 \[Pi]}, PlotStyle -> None, MeshFunctions -> {#3 &},
Mesh -> {{{\[Pi]/2, Directive[Opacity, Blue, Thick]}}}],
Line[data_] :> data, -4, 1][];
SetDirectory[NotebookDirectory[]];
Export["Groov_pro_Diff_THAf.txt", data, "Table"]

Through the above code, although I generate a txt file, I get the error

Part1 of {} does not exist

I have no issues with the plot, ParametricPlot[...] command gives me the correct figure, but not during saving the data. Here I would like to save the data as two columns only. Can anyone suggest how to extract the data in such a case?