Question 5
Given
$$(\cos27^\circ+\cos99^\circ+\cos117^\circ+\cos189^\circ)^2=\frac mn,$$
where $m,n$ are relatively prime positive integers, find $m+n$.
$$(\cos27^\circ+\cos99^\circ+\cos117^\circ+\cos189^\circ)^2=\frac mn,$$
where $m,n$ are relatively prime positive integers, find $m+n$.