What is the difference between "subtlety", "nuance", and "nicety"?

Source: DICTIONARY.com

DEFINITIONS:

1. SUBTLETY: a small but important detail; the quality or state of being subtle or hard to notice

2. NUANCE: a very slight difference in appearance, meaning, sound, etc.

3 NICETY: a detail or small difference that is only obvious after careful thought

EXAMPLES:

1. SUBTLETY:

All the subtleties of the music are conveyed in this new recording.

Listening to the interview, I was impressed by the subtlety of the questions.

1. NUANCE:

The painter has managed to capture every nuance of the woman's expression.

Linguists explore the nuances of language.

1. NICETY: They spent a lot of time arguing about legal niceties.

We don't bother with all the social niceties here