Star inside pentagon

Geometry Level 4

The picture above shows a regular pentagon \(ABCDE\), with area of \(T\). Five equilateral triangles of side length \(AB\) were constructed inside the pentagon, example the triangle \(ABF\). The overlapping regions were shaded, and its area is denoted as \(U\).

Find \(\displaystyle \left \lfloor \frac{1000U}{T} \right \rfloor\).

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