There exist two ordered triples \((a,b,c)\) for which \(4x^2-4xy+ay^2+bx+cy+1=0\) represents a pair of identical straight lines in the \(xy\)-plane.

If these triples are \((a_1,b_1,c_1)\) and \((a_2,b_2,c_2)\), then find the value of \(a_1+b_1+c_1+a_2+b_2+c_2\).

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