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∑k=135sin(5k∘)=tan(mn)∘\large \sum_{k=1}^{35} \sin \left(5k^\circ \right) = \tan \left(\frac {m}{n}\right)^\circk=1∑35sin(5k∘)=tan(nm)∘.
The equation above holds true for coprime positive integers mmm and nnn, where mn<90\dfrac {m}{n} < 90nm<90. Find m+nm+nm+n.
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