Also Nepal is UTC+5:45, and there is a sparsely populated region of Australia – around the settlement of Eucla, on the border between the states of Western Australia and South Australia – which unofficially observes UTC+8:45, although that is not its legal time zone.
Historically even weirder offsets have been used:
UTC-00:44 – Liberia, 1919–1972
UTC+04:51 – Bombay (now Mumbai), India, prior to 1955
UTC+05:40 – Nepal, 1921–1986
UTC+07:20 – daylight saving time in Malaya (now Malaysia's peninsular region) and Singapore, 1933–1941
But at least all of those were to the minute. In the past, some places have even used offsets to the second:
UTC-00:43:08 – Liberia, prior to 1919
UTC-00:25:21 – Ireland, 1880–1916
UTC+05:41:16 – Nepal, prior to 1920
Most software probably handles minute-based offsets correctly, even weird ones which aren't on the hour/half-hour/quarter-hour mark, but very little software would support seconds-based offsets. Prior to the introduction of standardised time zones, people used mean local solar time – which can be defined to as precise an accuracy as you'd like, down to the second, even the sub-second, provided you have a sufficiently accurate measurement of your location – and some early attempts at time zones just used the capital's local mean solar time down to the nearest second, hence the seconds-based offsets. Most clocks were not very accurate in those days, rendering the seconds-based offset largely theoretical. I doubt anybody is going to do that again.
The most crazy is of course the Netherlands between 1909 and 1937, with an offset of 19 minutes and 32.13 seconds (the tzdb excludes the .13 seconds as that's not supported). Not sure if there's been other timezones with subsecond definitions.
Historically even weirder offsets have been used:
UTC-00:44 – Liberia, 1919–1972
UTC+04:51 – Bombay (now Mumbai), India, prior to 1955
UTC+05:40 – Nepal, 1921–1986
UTC+07:20 – daylight saving time in Malaya (now Malaysia's peninsular region) and Singapore, 1933–1941
But at least all of those were to the minute. In the past, some places have even used offsets to the second:
UTC-00:43:08 – Liberia, prior to 1919
UTC-00:25:21 – Ireland, 1880–1916
UTC+05:41:16 – Nepal, prior to 1920
Most software probably handles minute-based offsets correctly, even weird ones which aren't on the hour/half-hour/quarter-hour mark, but very little software would support seconds-based offsets. Prior to the introduction of standardised time zones, people used mean local solar time – which can be defined to as precise an accuracy as you'd like, down to the second, even the sub-second, provided you have a sufficiently accurate measurement of your location – and some early attempts at time zones just used the capital's local mean solar time down to the nearest second, hence the seconds-based offsets. Most clocks were not very accurate in those days, rendering the seconds-based offset largely theoretical. I doubt anybody is going to do that again.