justone:
Maybe print an optical encoder wheel to attach underneath the table and use a reflective sensor to detect.
+1
A variation on this would be to print a strip that attaches to the edge of the turntable. It may be easier to install the photo-detector beside the turntable rather than under it. Som of the record turntables (remember them) used this technique to maintain the correct speed.
Remember that detecting the exact position will be a lot easier than making the turntable stop at a predetermined location.
...R