4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{376d12ab-022c-4070-a1e0-88eacc2fe48e-2_451_357_1672_852}
\captionsetup{labelformat=empty}
\caption{Figure 1}
\end{figure}
A small smooth ball \(B\), moving on a horizontal plane, collides with a fixed vertical wall. Immediately before the collision the angle between the direction of motion of \(B\) and the wall is \(2 \theta\), where \(0 ^ { \circ } < \theta < 45 ^ { \circ }\). Immediately after the collision the angle between the direction of motion of \(B\) and the wall is \(\theta\), as shown in Figure 1.
Given that the coefficient of restitution between \(B\) and the wall is \(\frac { 3 } { 8 }\), find the value of \(\tan \theta\).
(8)