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On the sides \( \mathrm { AB } \) and \( \mathrm { AC } \) of triangle \( \mathrm { ABC } , \) equilateral triangles \( \mathrm { ABD } \) and \( \mathrm { ACE } \) are drawn. Prove that: (i) \( \angle \mathrm { CAD } = \angle \mathrm { BAE } \) (ii) \( \mathrm { CD } = \mathrm { BE } \) .

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