Let a vertical tower $AB$ have its end $A$ on the level ground. Let $C$ be the mid-point of $AB$ and $P$ be a point on the ground such that $AP = 2AB$. If $\angle BPC = \beta$, then $\tan\beta$ is equal to:\\
(1) $\dfrac{6}{7}$\\
(2) $\dfrac{1}{4}$\\
(3) $\dfrac{2}{9}$\\
(4) $\dfrac{4}{9}$