A V-shaped tube attached to the ground with its vertex. It's one leg makes an angle of $30 ^\circ$, and the other leg makes an angle of $60 ^\circ$ with the horizontal. The tube is filled with a liquid in a total length of $1\text{ m}$. Now the liquid at one side is displaced a little.Find the Time - period of SHM.

Your answer can be represented as $\sqrt{\dfrac{a \pi^b}{c (\sqrt{d} + 1)}} \; ,$

where $a,b,c$ and $d$ are positive integers with $a,c$ coprime and $d$ square-freee.

Enter your answer as $a + b + c + d$.

**Details and Assumptions**:

Neglect surface tension , viscuous force and friction.

$g = 10\text{ m/s}^2$.