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A smooth circular cylinder of radius $$\displaystyle b$$ is fixed parallel to a smooth vertical wall with its axis horizontal at distance $$\displaystyle c$$ from the wall. A smooth uniform heavy rod of length $$\displaystyle 2a$$ rests on the cylinder with one end on the wall in a vertical plane perpendicular to the wall. Show that its inclination $$\displaystyle \theta$$ to the horizontal is given by

$$\displaystyle a\cos^3\theta+b\sin^3\theta=c$$