Consider the parabola with vertex \( \left( \frac{1}{2}, \frac{3}{4} \right) \) and the directrix \( y = \frac{1}{2} \). Let \( P \) be the point where the parabola meets the line \( x = -\frac{1}{2} \). If the normal to the parabola at \( P \) intersects the parabola again in the point \( Q \), then \( (PQ)^2 \) is equal to:
