A container filled with liquid moves down a rough fixed inclined plane with constant acceleration as shown in figure above.

The angle of incline is \( \cos^{-1} \frac{3}{5} \) and the liquid surface makes an angle of \( \cos^{-1} \frac{4}{5} \) with the horizontal.

If the coefficient of friction can be written as \(\dfrac ab\) where \(a,b\) are coprime positive integers, find \(a+b\).

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