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When Alpha is zero, it does not matter what the angles are (as they are multiplied by zero).
When Alpha > 0 (separation between the wings is larger than the radius of the wings) the lowest energy state should be when theta equals to 0/180 degrees as that keeps the energy negative.
When Alpha < 0 (separation between the wings is smaller than the radius) the lowest energy state becomes 90/270 as that keeps the energy negative,
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