A solid cube is divided into two pieces by a single rectangular cut. As a result, the total surface area increases by a fraction of the surface area of the original cube.
What is the greatest possible value of ?
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\frac{1}{3}
\frac{\sqrt{3}}{4}
\frac{\sqrt{2}}{3}
\frac{1}{2}
\frac{1}{\sqrt{3}}
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