4.

\begin{figure}[h]
\begin{center}
  \includegraphics[alt={},max width=\textwidth]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-12_428_897_251_593}
\captionsetup{labelformat=empty}
\caption{Figure 2}
\end{center}
\end{figure}

A particle of weight $W$ lies on a rough plane.The plane is inclined to the horizontal at an angle $\alpha$ where $\tan \alpha = \frac { 3 } { 4 }$ .The coefficient of friction between the particle and the plane is $\frac { 1 } { 2 }$ The particle is held in equilibrium by a force of magnitude 1.2 W .The force makes an angle $\theta$ with the plane,where $0 < \theta < \pi$ ,and acts in a vertical plane containing a line of greatest slope of the plane,as shown in Figure 2.
\begin{enumerate}[label=(\alph*)]
\item Find the value of $\theta$ for which there is no frictional force acting on the particle.

The minimum value of $\theta$ for the particle to remain in equilibrium is $\beta$
\item Show that

$$\beta = \arccos \left( \frac { \sqrt { 5 } } { 3 } \right) - \arctan \left( \frac { 1 } { 2 } \right)$$
\item Find the range of values of $\theta$ for which the particle remains in equilibrium with the frictional force acting up the plane.
\end{enumerate}

\hfill \mbox{\textit{Edexcel AEA 2017 Q4 [13]}}