\[\Large \prod_{n=1}^{\infty} \left(1-\frac{1}{\phi^n}\right)^{[\mu(n)-\varphi(n)]/n}\]

What is the value of the product above?

Note: \(\varphi\) is the Euler totient function, \(\mu\) is the Moebius function, and \(\phi = \dfrac{1+\sqrt5}{2}\) is the golden ratio.

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