# Equal sins

Geometry Level 3

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

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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