\({v^2} = {u^2} + 2al/2 = 2(g\sin \theta )l/2 = gl\sin \theta \)

For lower half

\(⇒\) \(0 = {u^2} + 2g(\sin \theta - \mu \cos \theta )\frac{l}{2}\)

\(⇒\) \( - gl\sin \theta = gl(\sin \theta - \mu \cos \theta )\)

\(⇒\) \(\mu \cos \theta = 2\sin \theta \Rightarrow \mu = 2\tan \theta \)