$ k = 3 $: $ 470^\circ $ → too large
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- $ k = 0 $: $ 110^\circ $
- $ k = 1 $: $ 230^\circ $
- $ k = 2 $: $ 350^\circ $
- The solutions in $ [0^\circ, 360^\circ] $ are:
- \theta = 10^\circ, 110^\circ, 130^\circ, 230^\circ, 250^\circ, 350^\circ
- 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.
