# Tail estimates for the sum $\sum_{n\geq 1} (1/ \varphi(n)^2)$

I've been trying to prove the following fact: If $$\varphi$$ denotes Euler's totient function, then for $$Q\geq 1$$ we have \begin{align*} \sum_{n\geq Q} \frac{1}{\varphi(n)^2} \ll Q^{-1}. \end{align*} I am able to prove that $$\sum_{n\geq Q} \frac{1}{n^2} \ll Q^{-1},$$ and I'm familiar with Euler products but unclear on the best way to apply them here. I am also aware of the estimate $$\varphi(n)\gg n/\log (\log(n))$$. Any hints would be really helpful! Do I need to use some kind of averaging argument for $$\varphi?$$