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The case of Miranda v. Arizona is significant because it established the requirement that individuals taken into police custody must be informed of their rights under the Fifth and Sixth Amendments. Specifically, this includes the right to remain silent and the right to an attorney.

This requirement emerged after Ernesto Miranda was interrogated by police without being made aware of his rights, leading to a confession that was used against him in court. The Supreme Court ruled that this lack of notification violated Miranda's rights, reinforcing the necessity of the "Miranda warning." This warning aims to ensure that individuals are aware of their rights to avoid self-incrimination and to have legal counsel, thereby protecting the integrity of the judicial process.

The other cases listed do not involve the advisement of rights during police arrests. U.S. v. Nixon dealt with presidential power and executive privilege, Engel v. Vitale addressed the role of school-sponsored prayer and the Establishment Clause, and McCulloch v. Maryland focused on federal versus state powers over banking. Each of these cases, while important, does not pertain to the rights of individuals upon arrest, making Miranda v. Arizona the correct and relevant case in this context.