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\frac{2}{3}\times \frac{1+\sqrt{3}}{2}
Since \frac{1}{2} and \frac{\sqrt{3}}{2} have the same denominator, add them by adding their numerators.
\frac{2\left(1+\sqrt{3}\right)}{3\times 2}
Multiply \frac{2}{3} times \frac{1+\sqrt{3}}{2} by multiplying numerator times numerator and denominator times denominator.
\frac{\sqrt{3}+1}{3}
Cancel out 2 in both numerator and denominator.