Let \(f(x)\) be a polynomial of degree greater than 3 which when divided by \((x-1)^2\) and \((x-3)\) leave remainders \((2x-1)\) and \(15\) respectively.

If \(f(x)\) when divided by \((x-1)^2(x-3)\) leaves a remainder of the form \(ax^2+bx+c\), then find the value of \(a+2b\) is :

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