Regular Partitioning

Geometry Level 3

In a regular hexagon \(ABCDEF\), points \(W\), \(X\), \(Y\), and \(Z\) are on sides \(CD\), \(BC\), \(AF\), and \(EF\), respectively, in a way such that \(AB\), \(WZ\), \(XY\), and \(ED\) are parallel and equidistant. If the side length of \(ABCDEF\) is 1, what is the area of hexagon \(WCXYFZ\)?

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