Three smooth identical cylinders \( A, B \) and \( C \) are placed on smooth inclined plane show...

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Three smooth identical cylinders \( A, B \) and \( C \) are placed on smooth inclined plane shown in the figure. The minimum value of \( \tan \theta \) that prevent the arrangement from collapse is \( \frac{1}{3 \sqrt{n}} \). Find the value of \( n \).
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