I don't really know, I am currently farting around with blender trying to see, but that is far from rigorous. and going poorly. but let me explain my thought process.

Note the egg shape in the article. specifically the widest band around the equator. now imagine one passing straight down through the other. one edge ring would pass through the shadow if it has a slight rotation offset but it is blocked by the next edge ring up, which could also fit but requires a different offset, so if you could change that rotational offset while it is passing through would it fit?