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If a, b, c are real numbers, then prove that |(a,b,c)(b,c,a)(c,a,b)| = -(a+b+c)(a+bω+cω2)(a+bω2+cω), where ω is a complex number and cube root of unity.

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(a,b,c)(b,c,a)(c,a,b)| = -(a+b+c (a+bω+cω2)(a+bω2+cω),

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