The line \( x = 8 \) is the directrix of the ellipse \( E : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 \) with the corresponding focus \( (2, 0) \). If the tangent to \( E \) at the point \( P \) in the first quadrant passes through the point \( (0, 4\sqrt{3}) \) and intersects the \( x \)-axis at \( Q \), then \( (3PQ)^{2} \) is equal to ______.
