Trignometric Series

Geometry Level 4

\[ S = \cos \left( \frac{2 \pi}{28} \right) \csc \left( \frac{3 \pi}{28} \right) + \cos \left( \frac{6 \pi}{28} \right) \csc \left( \frac{9 \pi}{28} \right) + \cos \left( \frac{18 \pi}{28} \right) \csc \left( \frac{27 \pi}{28} \right) \]

Find the value of \( \left| \log_{2 - \sqrt{3}} \left( 1 + S + S^{2}\right)\right| \).

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