4.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{05b21c5d-5958-4267-b1e6-3d1ed20d5609-12_428_897_251_593}
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\caption{Figure 2}
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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.
（a）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 \(\beta\)
（b）Show that
$$\beta = \arccos \left( \frac { \sqrt { 5 } } { 3 } \right) - \arctan \left( \frac { 1 } { 2 } \right)$$
（c）Find the range of values of \(\theta\) for which the particle remains in equilibrium with the frictional force acting up the plane．