# Precarious cylinders

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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