I printed with a 0.6 nozzle, but 0.4 will also work.
Both parts can be printed at the same time but I suggest printing the threads at 0.2mm layerheight and 100% infill. And dont tighten it to much in the camera.
I created 0.4 and 0.6 nozzle Gcode files, and both of them have the threads to be a finer layerhight.