If AABC having vertices A(a cos 0₁, a sin 0₁), B(a cos 02- a sin 0₂), and C(a cos 03, a sin 03) is equilateral, then prove that cos ₁+ cos 0₂ + cos 03 = sin 0, + sin 0₂2 + sin 0₂ = 0.

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