Final answer:
The Supreme Court case that approved the separation of guilt determination from sentencing determination is not given, but is related to the bifurcated trial process used in capital punishment cases. Notable cases related to this process are Furman v. Georgia and Gregg v. Georgia.
Step-by-step explanation:
The specific Supreme Court case where the separation of the determination of guilt from the determination of the sentence was approved is not explicitly provided in the context given. Such separation usually pertains to the bifurcated trial process, which is a two-part trial structure used to first determine guilt or innocence, and then to determine the appropriate sentence. This occurs often in capital punishment cases where the death penalty is a possible outcome. While not mentioned in the provided text, one of the most notable cases establishing this precedent is the Furman v. Georgia (1972) decision, which led to a temporary halt of capital punishment in the United States, and required states to separate the sentencing phase from the guilt phase to avoid arbitrary sentencing. Following cases like Gregg v. Georgia (1976) reaffirmed this by allowing the death penalty under revised state laws that addressed the court's concerns. The provided references to cases such as Gideon v. Wainwright and Breard v. Greene deal with the right to legal counsel and international jurisdiction in capital cases, but neither explicitly addresses the separation of trial phases.