Let chord \( PQ \) of length \( 3\sqrt{13} \) of the parabola \( y^2 = 12x \) be such that the ordinates of points \( P \) and \( Q \) are in the ratio \( 1:2 \). If the chord \( PQ \) subtends an angle \( \alpha \) at the focus of the parabola, then \( \sin \alpha \) is equal to:
