Final answer:
The détente period with the Soviet Union ended with the Cuban Missile Crisis in 1962.
Step-by-step explanation:
The period of détente with the Soviet Union ended with the Cuban Missile Crisis. In 1962, the United States and the Soviet Union came to a tense diplomatic confrontation over the presence of Soviet missiles in Cuba. This event marked a turning point in the Cold War and demonstrated the brinkmanship between the two superpowers.