\[4\sin \frac{\alpha}{2}+3\sin \frac{\beta}{2}+2\sin \frac{\gamma}{2}+\sin \frac{\delta}{2}\]

Let \(\alpha\), \(\beta\), \(\gamma\), and \(\delta\) be some small positive angles in ascending order of magnitude which has their sines equal to a positive quantity \(k\). Find the value of the above expression.

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