# Professor $$\mathfrak{X}$$ and his experiments! -3

Professor $$\mathfrak{X}$$ is doing now an another experiment related to Rotational mechanics. He took a uniform stick of length L and mass M and hinged it at one end . Then he released the stick from rest at an angle $$\theta_{o}$$ with the vertical. He found that, when the stick makes an angle $$\theta$$ with the vertical, the hinge exerts a force $$\text{F}_{r}$$ along the stick, $$\text{F}_{t}$$ perpendicular to stick and acceleration due to gravity is g. If, $\text{F}_{r} = \dfrac{a}{b} \text{Mg} ( c\cos\theta - d\cos\theta_{o} )$ and $\text{F}_{t} = \dfrac{e}{f} \text{Mg} \sin\theta$. Find the value of $\text{a+b+c+d+e+f}$

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