What's the timezone of Easter Island and why?

I'm a big fan of daft little timezones. There's a weird little one in Australia called Central Western Standard Time, which is set at 8h45mins ahead of UTC, with no daylight saving. This is an attempt to compromise between Central and Western time, and avoid the fact that otherwise you jump two and a half hours in one go passing from Western to Southern Australia at certain times of year. The population of the area covered by CWST is about 200.Russia used to have some tiny little timezones until very recently, but the Federal government sadly abolished them - this does mean there are a few two-hour jumps in Russia though.

Half hours aren't that special - there are quite a few, and a large percentage of the worlds population is on a 1/2 hour offset, since Indian Standard Time is UTC + 5 1/2. The special cases are the quarter hours. I mentioned the little Aussie one before - there's also the New Zealand territory of the Chatham Islands, whose time is set at 13 hours 45 minutes ahead of UTC, and I think some uninhabited US owned islands in the Pacific have a similar timezone.These are sparesly inhabited places, so it doesn't matter to many people, but Nepal deserves special mention as being the only proper country to do this. Nepal time is 5h45 ahead of UTC - because why not?