Only a third are coprime?

Let \(x_1, x_2, x_3, \ldots \) be all the distinct positive integers satisfying \(\phi(x) = \dfrac x3\).

Compute \(\dfrac1{x_1} + \dfrac1{x_2} + \dfrac1{x_3} + \cdots \).

\(\)
Notation: \(\phi(\cdot) \) denotes the Euler's totient function.

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