Rule reminder

All three mean 'to start doing', but differ in nuance: 'cominciare a / iniziare a + inf' = to begin, to start (neutral, any context); 'mettersi a + inf' = to suddenly/energetically start doing something, often with emotion or unexpectedness. 'Mettersi a' implies a change of state, sometimes urgency or spontaneity. Example: 'Ha cominciato a piovere' (neutral — it started raining); 'Si è messa a piangere all'improvviso' (she suddenly burst into tears — emotional, unexpected).