Full Sun - Half Moon?

[Cyberman]

Well... Eclipses require things to be lined up along the plane of the earth's orbit, you can have a 0/180 degree alignment along the lunar orbital plan and not have things line up correctly. That's why, even though 0/180 alignments occur every lunar orbit, eclipses are less frequent.

hehe, hence my distinction between ~180 and exactly 180.
~180 is when the two planes don't align... exactly 180 is when they align and you get an exact 180º, using the Earth as the center.

Not quite, as CD correctly pointed out. Your model confuses the Earth-Moon plane with the Sol-Earth plane. We still get the whole 180 thing with the E-M plane even when the S-E one doesn't align with it. It's a bit like me, standing at our fourth-floor window, watching two cats in the street circling each other (or if it's a Friday night, two lasses in tube tops and belt skirts circling and hissing about someone called Gary). From here, I can see the two of them no matter where each of them are in their orbit of each other. If I went downstairs and got to their eye-level, they would eclipse each other every time they reached the 180 points relative to my eyeline.

Here's one to shit up the theists though: another word for one body (planet, moon etc) eclipsing another is 'occultation'.