Angua entered the Discworld series at the beginning of Men at Arms, the second Watch book. Remember, this was after the innovative Guards! Guards! and before the Watch had become a plc and a registered trademark, generating sales of the books on a regular basis.
The Watch benefits enormously from having a lycanthropic member, who can fill the role of both police woman and police dog.
In Men at Arms we see the Watch recruiting to try to reflect the cosmopolitan nature of Ankh-Morpork. There is some comment as this tall, blonde, attractive, intelligent person dons her badge. Reference is made to the fact that her abilities will be impaired for a few days each month, along with the objection that 'for gods sake, she's a W...', steering the reader to suspect some masoganistic resentment. However soon enough we discover that the problem is that Angua is in fact a werewolf.
Angua replaces Terry's prototype female werewolf Ludmilla Cake, and clearly owes a debt of inspiration to Conina the Barbarian Hairdresser and perhaps even Herrena.
The most recent Discworld story (TFE) gives Angua her most prominent role yet. Angua's family are from the Uberwald, an evocatively named region where vampire and werewolf nobility prey on terrified villagers. Angua, of course, doesn't share her relations' predatory contempt for normal people. No, she uses her powers for good, in the Watch.
The Watch benefits enormously from having a lycanthropic member, who can fill the role of both police woman and police dog. When miscreants offer resistance she can threaten to tear them to shreds, although naturally she never actually does so. Plus, she has to get naked every time she changes form! Though whenever she's changing back into human form she demurely does so out of sight, and everyone's really discrete about not embarrassing her.
A romantic attachment has grown up between Angua and Carrot, and if you think about it, this makes sense. Carrot is the closest thing to a classic 'hero' that the Discworld has got: big, strong, heir to the throne - yet considerate, fair and sometimes comically bashful. Angua compliments these traits nicely: she is also big, strong - and yet pleasingly remorseful about her inherited condition.
WB adds: However, we have a problem. It's to do with lunar cycle/period jokes. It's to do with breastplates. It's to do with strong yet vulnerable women characters. And above all, it's to do with my increasing resentment and bitterness towards attractive women.
You would have thought that if any fantasy series could be relied upon to be disrespectful or anarchic it was the Discworld. Not where beautiful women are concerned. Generally the only people who are really rude to women are brutal thugs who get their come-uppance two paragraphs later. People are rude to Vimes, or Rincewind, or the Archchancellor all the time, but none of her colleagues like to criticise Angua. Because she's a werewolf? No. Because she's a looker.
Perhaps this is what I really don't like about Angua - the good looking types succeed all the time in real life. Is it fair that they should on the Discworld, too? When was the last time Rincewind pulled, hmm?
RM adds: The whole point of Angua is that she is so straight - a sane person in an insane world. It isn't always possible to relate to the actions of a semi intelligent troll or a cowardly wizard etc. Angua can be depended on to react to any situation in the same way as the reader might (except the transforming into a dog bit, of course) as opposed to some humerous exageration.
As for her treatment in general, I think that here we have a character which Terry likes. Similar to Carrot, Vimes, Verance, the list goes on, we readers are supposed to like them too. And why not?