Think De Moivre

Geometry Level 2

Let aa and bb be positive integers such that 1cos(80)+isin(80) \dfrac1{\cos(80^\circ) + i \sin(80^\circ) } can be written in the form of cos(a)isin(b) \cos(a) - i \sin(b) , where aa and bb are minimized, calculate aba - b.

Note: Angles are measured in degrees.

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