If \( a \) and \( b \) are real numbers between 0 and 1 such that t...

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If \( a \) and \( b \) are real numbers between 0 and 1 such that the points \( (a, 1),(1, b) \) and \( (0,0) \) form an equilateral triangle, find \( a \) and \( b \).
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