Three identical rigid circular cylinders A , B and C are arranged on smooth inclined surfaces as shown.

The **least** value of \(x\) that prevent the arrangement from collapsing can be expressed as \( \tan^{-1} \dfrac a{3^{c/d}} \), where \(a,c\) and \(d\) are positive integers with \(c,d\) coprime.

Submit your answer as \(a+c+d\).

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