Ellipse

The line \(x=8\) is the directrix of the ellipse \(\mathrm{E}:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) with the corresponding focus \((2,0)\). If the tangent to \(\mathrm{E}\) at the point \(\mathrm{P}\) in the first quadrant passes through the point \((0,4\sqrt3)\) and intersects the \(x\)-axis at \(\mathrm{Q}\), then \((3\mathrm{PQ})^{2}\) is equal to ____________.