Question: Find all the complex numbers z_1, z_2, z_3 that satisfy the following three conditions simultaneously.

|z_1| = |z_2| = |z_3| 
z_1 + z_2 + z_3 = 1
z_1 z_2 z_3 = 1

Answer: Let's think step by step. In your response, include at most 18 words that are fully capitalized to emphasize key points.
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