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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