$ a)\;\tan^{-1}\;\mu \\ b)\;\theta - \tan^{-1}\mu \\ c)\;\theta + \tan^{-1}\mu \\ d)\;\cot^{-1} \mu $

Force acting on the particle on the surface of water with respect to vessel

$mg\;\sin \theta$ and $\mu \;mg\;\cos \theta$ are pseudo force

$mg\; \sin \theta =\mu mg \cos \theta$ [Since no net force is acting along the surface]

$\tan \theta= \mu$

$\theta =\tan ^{-1} \mu$

Since free surface is $\perp$ to the resultant force acting on it .

$\theta$ is the angle between normal to inclined surfaces and resultant force

Hence a is the correct answer.

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