Let $P Q$ be a focal chord of the parabola $y ^ { 2 } = 4 a x$. The tangents to the parabola at $P$ and $Q$ meet at a point lying on the line $y = 2 x + a , a > 0$.
If chord $P Q$ subtends an angle $\theta$ at the vertex of $y ^ { 2 } = 4 a x$, then $\tan \theta =$
(A) $\frac { 2 } { 3 } \sqrt { 7 }$
(B) $\frac { - 2 } { 3 } \sqrt { 7 }$
(C) $\frac { 2 } { 3 } \sqrt { 5 }$
(D) $\frac { - 2 } { 3 } \sqrt { 5 }$