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

Let `a ,\ b ,\ c` be three non-zero real numbers such that the equation `sqrt(3)\ acosx+2\ bsinx=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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