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Let a, b, c, be three non-zero real numb...

Let a, b, c, be three non-zero real numbers such that the equation `sqrt(3)a cos x+2b sin x=c, x in [-pi/2, pi/2]`, has two distinct real roots `alpha` and `beta` with `alpha+beta=pi/3`. Then, the value of `b/a` is ________.

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