I don't know about any zones with three-quarter hour offsets, but would like to know what they are.
From the same usno1989 file (which is outdated and contains errors, but seems to be the most comprehensive source we have):
NEPAL 5H45M AHEAD OF UTC NEW ZEALAND 12H45M AHEAD OF UTC CHATHAM ISLAND In the Rand-McNally atlas there are a few other Pacific islands with 40 mins offsets, all of which appear as full or half-hour zones in the file; it also lists Nepal at GMT+5:40 and Liberia as -0:44 (yes, forty four) -- makes sense since Monrovia is at exactly 11 degrees west, but probably outdated too. Amos Shapir Net: amos@cs.huji.ac.il Paper: The Hebrew Univ. of Jerusalem, Dept. of Comp. Science. Givat-Ram, Jerusalem 91904, Israel Tel: +972 2 585706 GEO: 35 11 46 E / 31 46 21 N