Three blocks placed on top of each other are on a plane inclined at an angle of \(30^{\circ}\) with respect to horizontal. The top and bottom blocks are connected by a string that goes over a pulley. The top block has a mass of \(30\text{ kg}\), the middle one a mass of \(40\text{ kg}\), and bottom one a mass of \(50\text{ kg}\).

If the coefficient of static friction \(\mu_{\text{s}}\) is the same between all the pairs of surfaces, then find the minimum value of \(\mu_{\text{s}}\) such that the blocks remain in equilibrium.

Give your answer to 3 decimal places.

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