A semi circle of diameter 1 unit sits at the top of a semi circle of diameter 2 units. the shaded region inside the the semi circle but outside the larger semi circle is called a **lune**. If the area of the lune is \(\alpha\), then find the value of
\[\lfloor 1000\alpha\rfloor\]

**Note**

- Assume that the diameters are parallel to each other.

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