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Given the ellipse:

$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$

where $a > 0$ and $b > 0$, three points $(x_1, y_1)$ , $(x_2, y_2)$ , and $(x_3, y_3)$ are chosen to lie on it. What is the maximum area of the triangle formed by these three points?

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