Two charges are placed along same horizontal line. Charge1 is carrying charge \(Q\). whereas charge 2 is carrying charge \(q\).If the field line emerging from charge 1 at an angle \(A=30^\circ \) with horizontal goes to infinity and the tangent to that field line at infinity from charge 2 makes an angle \(B=60^\circ\) with horizontal.

If \(\dfrac Qq\) is of form \(\dfrac{\sqrt a-b}{c}\), where \(a,b\) and \(c\) are positive integers with \(c\) minimized, find \(a+b+c\).

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