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A force of Cuban exiles, which trained by the CIA, aided by the United Sates government attempted to invade Cuba and overthrow the Communist government of Fidel Castro. However, the attempt failed.
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US spy plane reported sighting the construction of Soviet nuclear missile base in Cuba. President Kennedy set up a naval blockade and demanded the removal of the missile. War was averted because the Russian agreed to remove the weapons. Then the United States also agreed not to invade Cuba.
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North Vietnamese torpedo boats allegedly fire on the American warship USS Maddox. As the result of the incident the United States became directly involved in the Vietnam War. https://alphahistory.com/coldwar/cold-war-timeline-1960-69/
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Operation Rolling Thunder was a demonstration of America’s near total air supremacy during the Vietnam War. It was started in an effort to demoralise the North Vietnamese people and to undermine the capacity of the government in North Vietnam to govern. Operation Rolling Thunder failed on both accounts. https://www.historylearningsite.co.uk/vietnam-war/operation-rolling-thunder/
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On September 1971 during the period of Detente, the Four Powers Agreement on Berlin was signed by the United States, the Soviet Union, Great Britain and France. It reestablished travel and communications between East and West Berlin, and contributed to the easing of tensions between the Western and Soviet blocs. https://alphahistory.com/coldwar/four-powers-agreement-berlin-1971/