Simplify
\[\frac{\sin 10^\circ + \sin 20^\circ + \sin 30^\circ + \sin 40^\circ + \sin 50^\circ + \sin 60^\circ + \sin 70^\circ + \sin 80^\circ}{\cos 5^\circ \cos 10^\circ \cos 20^\circ}.\]The answer is in the form k\sqrt{m}+n,. Please provide the value of k + m + n.

Let's think step by step and output the final answer within \boxed{}.
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