Consider two fixed points \(F'\) and \(F\) so that \(F' F = 4\).

Let \(M\) be a variable point. Denote \(K \) and \(L \) to be the respective orthogonal projections of \(F\) and \(F'\) on the bisector of the angle \(F' \hat M F \).

Assume that \(F' \hat M L = F \hat M K = \alpha\), and \(FK \times F' L = 3\). Find \((MF - MF')^2 \).

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