Paragraph: Let $PQ$ be a focal chord of the parabola $y^2 = 4ax$. The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y = 2x + a$, $a > 0$.

If chord $PQ$ subtends an angle $\theta$ at the vertex of $y^2 = 4ax$, then $\tan\theta =$