I didn't see that interpretation for "tan" anywhere (perhaps it's slang?). I'm no expert; like I said the only reason I posted was because no actual experts seemed to be paying attention, and I at least happen to have a Kanji dictionary handy. I'm sure I'm being quite pretentious by even attempting a rough translation. :
My reasoning went something like this:
gekka = getsu (moon) + ka (down/under) (the "tsu" becomes a consonant doubler in the compound) = "in the moonlight" (cf. "under the moon")
mugen = mu (nothing/without) + gen (end) = infinite/endless (on a rather unrelated topic, this meaning is presumably the inspiration for the name of the famous user-extensible fighting game engine)
tan = grief/suffering (I guess the "spit" meaning might be tangentially related to this)
But without seeing the Kanji, it's really impossible to know for sure what the appropriate interpretation is.