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

**Note**: Angles are measured in degrees.

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