By Jacob Gronholt-Pedersen COPENHAGEN (Reuters) – Denmark’s soon-to-be king and queen have sought to balance their royal jobs with a modern family life and an engagement in progressive causes, helping keep the monarchy relevant and popular in the Nordic country. Crown Prince Frederik, 55, will take the throne on Sunday, following his mother Queen Margrethe II’s surprise announcement on live TV on New Year’s Eve that she would abdicate in favour of her oldest son. He will become King Frederik X and by his side will be Queen Mary, 51, an Australian-born former marketing and advertising director….