Regardless of what happened in 1906, Iran had a democratically elected government in 1953. Great Britain was concerned they would lose influence if the new government nationalized the oil fields, and got the US to help instigate a coup to remove the government.
Trump inherited this mess. Kudos to him for wanting to fix it, but either he is receiving some bad, even dishonest, advise, or he has an ace up his sleave. I hope it's the latter, for our sake as well as Iran's.
Great Britain is a bad ally. They got us involved in WWI which led to WWII and with the end of the Cold War and the emergence of the EU as the supranational government.
It is par for the course that they got us into Iran way back in 1953.
Finally President Trump has the appropriate relationship with Great Britain and we used to be that way before WWI.
We can trade with them but we shouldn't trust them on anything and of course we shouldn't try to overthrow governments throughout the world.
The shah was the head of government Iran, not Mosaddegh. Mosaddegh sax appointed by the shah, not elected as prime minister. Pahlavi had the constitutional authority to dismiss Mosaddegh, and he was violating the Iranian constitution by going outside his authority.
It was not a coup. These are facts.