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Angelo Mancuso is a police officer and an elaborate joke.
The most obvious part of the joke is that Mancuso is just not very good at his job. The first thing he does is try to arrest Ignatius for basically no reason, which winds up creating such a mess that his sergeant orders him to go undercover. Mancuso spends the rest of the book wearing ridiculous outfits, including fake beards and a Santa Claus suit, and for a while he is forced to stake out a bus station bathroom, where he contracts a horrible cold, and is humiliatingly robbed. Adding insult to injury, several times when he's shadowing people in his silly suits, he is reported to the police.
The second part of the joke, though, is that Mancuso suddenly triumphs through no fault of his own. He doesn't become a better police officer; he just ends up in the right place at the right time, wearing, for once, the right costume. He busts Lana Lee because she screws up and exposes herself, not because he does anything right. As his sergeant tells him, "'[…] just a couple days ago I was thinking you was a horse's ass'" (13.74), and the thing is, that despite this success, Mancuso is the same as he ever was.
In his trials and his philosophical perseverance in the face of bad luck and persecution, Mancuso is much more like Boethius than Ignatius is. Mancuso's vigil in the bathroom at the command of his sergeant is deliberately compared to Boethius's unjust prison sentence at the command of the king. The Consolation of Philosophy itself becomes part of the torture; Mancuso feels he has to read it because Ignatius gave it to him, but it just makes him "more depressed" (8.58). Boethius becomes one of the trials that Mancuso must stoically endure, until a better spin of Fortune's wheel.
It's worth noting, finally, that Mancuso is a pretty nice guy. Even if he does try to arrest Ignatius for no reason, through the rest of the book he mostly suffers quietly and tries to help out anyone he can—even Mrs. Reilly, who was involved in getting him into disgrace in the first place. "'We love him dearly'" (10.161), Dorian Greene says of Mancuso, and it's easy to see why. He seems to have a good heart, even when it's dressed up as a cowboy or a British tourist.