1. A laboratory apparatus contains a rough inclined plane that may be inclined at different angles to the horizontal.  When the plane is at an angle of ${ \theta }_{1}$ to the horizontal, where $0<{ \theta }_{1}<90^{\circ}$,  a small mass is released from rest on the plane and remains motionless.  After the angle is increased to ${ \theta }_{2}$,  where ${ \theta }_{2}<90^{\circ}$,  the same small mass is released from rest on the plane and begins to slide down the slope of the plane.

Show that

tan{ \theta }_{1}\leq \mu </p><p style="line-height: 1.7" class="text-lg tracking-wide font-normal leading-relaxed">where \(\mu is the coefficient of friction between the small mass and the plane.