If w and a² are the nonreal cube roots of unity and [1/(a + c)] + [1/(b + c)] + [1/(c + a)] = 2a² and [1/(a + @2)] + [1/(b + w²)] + [1/(c + w²)] = 2w, then find the value of [1/(a + 1)] + [1/(b + 1)] + [1/(c + 1)].

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