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Here we show that an upper bound on the error on $\\sin 2\\alpha$ due to penguin diagram effects can be obtained using only the measured rate $\\BR(B^\\pm \\to \\pi^\\pm \\pi^0)$ and an upper bound on the combined rate $\\BR(B \\to \\pi^0 \\pi^0) + \\BR(\\bar B \\to \\pi^0 \\pi^0)$. 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