HMMT 2018 U17

Compute the value of

$\frac{\cos 30.5^{\circ}+\cos 31.5^{\circ}+\ldots+\cos 44.5^{\circ}}{\sin 30.5^{\circ}+\sin 31.5^{\circ}+\ldots+\sin 44.5^{\circ}}$

Dataset text NuminaMath olympiads. Quoted with source.

Show the answer

2-\sqrt{2}-\sqrt{3}+\sqrt{6}

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