Star Moment

Consider a regular star inscribed in a unit circle, as shown in the figure above. The star wireframe has a uniform linear mass density, and the total mass of the star is \(M\).

If the moment of inertia of the star about the axis, passing through its center and perpendicular to its plane, can be expressed as \(\alpha M\), determine the value of \(\alpha\) to 3 decimal places.

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