3 alpha cases for double ring system

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    Viktor.VdB
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    Lowest quadrupole energy angle in 3 cases depending on alpha.

    Case 1: alpha=0
    Trivial energy of 0, angle is irrelevant.

    Case 2: alpha > 0 and Case 3: alpha < 0
    when (2cos^2(x)-sin^2(x)) = 0, solve for x

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