The curve defined by the parametric equations
\(x=\dfrac{t^2}{4}-1, \ y=\sqrt{3} t\), where \(0 \leq t \leq 2 \text {, }\)
is rotated about the \(x\)-axis to form an open hollow surface of revolution.
Find the surface area of the surface of revolution.
Give your answer in the form \(\pi\left(\dfrac{a \sqrt{b}}{c}-d\right)\), where \(a, b, c\) and \(d \in Z^{+}\).
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