Sliding Rod!

Rigid uniform Rod is pulled slightly ( Gently ) at the bottom at time \(t=0\) . Then Find the angle \(\theta \) from Horizontal as shown at which Rod will Loose it's contact with Vertical Smooth wall . If your answer can be expressed as : \(\tan { \theta } \quad =\quad \cfrac { a\sqrt { b } }{ c } \). Then Find \(a+b+c\)

Details and assumptions

\(\bullet\) All surfaces are perfectly smooth.

\(\bullet\) \(gcd(a,c)=1\)

\(\bullet\) \(b\) is square free integer and \(a , b , c\) all are integers.

This is Original
This is Part of my Set Deepanshu's Mechanics Blast

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