By Kate Holton, Elizabeth Piper and Alistair Smout LONDON (Reuters) -Rishi Sunak became Britain’s third prime minister in two months on Tuesday and pledged to lead the country out of a profound economic crisis and rebuild trust in politics. Sunak quickly reappointed Jeremy Hunt as his finance minister in a move designed to calm markets that had balked at his predecessor’s debt-fuelled economic plans. The former hedge fund boss said he would unite the country and was expected to name a cabinet drawn from all wings of the party to end infighting and abrupt policy changes that have horrified inve…