\theta = 10^\circ, 110^\circ, 130^\circ, 230^\circ, 250^\circ, 350^\circ
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- $ k = 2 $: $ 350^\circ $
- $ k = 3 $: $ 470^\circ $ → too large
- The solutions in $ [0^\circ, 360^\circ] $ are:
- The maximum value is $ \boxed{350^\circ} $. This corresponds to the peak resonance angle in the glacial oscillation model when physical constraints limit the domain to this interval.
- \boxed{350^\circ}
- Question: Compute $ \left( \cos \frac{2\pi}{7} + i \sin \frac{2\pi}{7} \right)^{14} + \left( \cos \frac{2\pi}{7} - i \sin \frac{2\pi}{7} \right)^{14} $, a quantity arising in modeling periodic synthetic microbial interactions in subglacial biofilm networks.
