Intersection between a plane and a surface in cylindrical coordinates

Question

I want to find the general expression for the intersection line of the following surfaces given in polar coordinates: $$ z=f(r,\theta) $$ $$ \theta=\pi/4 $$ where $f(r,\theta)$ is any real function in 3D cylindrical coordinates and the second surface is a vertical plane. Since the second plane equation is parallel to the $z$ axis, it doesn't have the $z$ term explicitly, but the intersection is assumed to occur. My question is on how can I express the intersection line for the general case of the first surface equation? Is it possible? Thank you in advance!