Sliding Rod!

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

Details and assumptions

\bullet All surfaces are perfectly smooth.

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

\bullet bb is square free integer and a,b,ca , b , c all are integers.

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

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