Using periodic boundary conditions for half-disk region in polar coordinates

Hi everyone,
I d like to apply a periodic condition in polar coordinates in physical surface 1 and physical surface 2. like in geometry below:

cl__1 = 1e+22;
Point(1) = {2.58819045102521, 9.659258262890679, 0, cl__1};
Point(2) = {-2.58819045102521, 9.659258262890679, 0, cl__1};
Point(3) = {3.88228567653781, 14.488887394336, 0, cl__1};
Point(4) = {-3.88230669953747, 14.4888817612239, 0, cl__1};
Point(5) = {0, 0, 0};
Circle(1) = {1, 5, 2};
Line(2) = {1, 3};
Circle(3) = {3, 5, 4};
Line(4) = {2, 4};
Line Loop(1) = {4, -3, -2, 1};
Plane Surface(1) = {1};
Extrude {0, 0, 10} {
Surface{1};
}
Physical Surface(1) = {21};
Physical Surface(2) = {13};

Can someone help to use periodic polar coordinates?

Observation: The angle between this planes is 30 degree, they are 15 and -15 degrees from plane ZY.