\[ \lim_{x\to2} \dfrac{\sqrt{1+\sqrt{2+x}} - \sqrt3}{x-2} \]

If the value of the limit above is equal to \( \dfrac 1{a\sqrt b} \), where \(a\) and \(b\) are integers with \(b\) square-free, find \(\dfrac{2016}{a\times b} \).

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