A uniform wire of resistance \(R\) is cut into four circular rings of equal radius. Rings are then connected such that their centers lie on the vertices of a square (as illustrated in the figure above).

If the equivalent resistance between \(A\) and \(B\) can be expressed as \(\frac{aR}{b}\), where \(a\) and \(b\) are coprime positive integers, determine the value of \(a+b\).

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