Brieftly explain how and why did decolonisation take place in Rhodesia when it was a lucrative and profitable market for the British empire?
It is actually too simplistic of to say, that Britain decolonized Rhodesia. What really happened is that Rhodesia's white government eventually gave way and allowed black majority control of the new country of Zimbabwe. Britain had opposed the independence of Rhodesia under a white government and pressured Rhodesia to allow true democracy.
Britain's motive for this was political and social. By the time that Ian Smith declared independence for Rhodesia in 1965, the world was turning against the idea of white domination of black majorities. Racism was becoming much less acceptable around the world. At the same time, Cold War politics meant that Britain needed to be concerned with the image that it projected. It did not want to give the impression that Western democracies approved of colonialism and racist regimes like that of Smith.
Thus, Britain pushed for majority rule in Rhodesia/Zimbabwe because it needed to do so for political and social reasons.