Why don't you simplify those fractions?

Geometry Level 2

\[ \displaystyle \sum_{k=1}^{145} \left [ \sin \left ( \frac {2\pi k}{8} \right ) - i \ \cos \left ( \frac {2\pi k}{14} \right ) \right ] = \frac {1}{\sqrt{a}} - i \cos \left ( \frac {\pi}{b} \right ).\] Find the sum of the positive integers \(a\) and \(b.\)

Note: \(i = \sqrt{-1}.\)

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