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 $\text{a+b+c+d+e+f}$