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.