\(a_{2}=g(\sin \theta+\mu \cos \theta)\)

\(\therefore \frac{1}{2} v _{0} \frac{ v _{0}}{ a _{1}}=\frac{1}{2}\left(\frac{ v _{0}}{2}\right)\left(\frac{ v _{0}}{2 a _{1}}\right)\)

\(\Rightarrow 3 \sin \theta=5 \mu \cos \theta\)

\(\therefore \mu=\sqrt{3} / 5\)