Let $V_n$ equal the number of visible points on the line $x + y = n$.
Given the Probability that two random numbers are coprime is $\frac{6}{\pi^2}$, we can state:
\begin{equation} \mathbb{E}[V_n] \approx \frac{6n}{\pi^2} \end{equation}
where $\mathbb{E}$ denotes the average value.
Next, Equating Euler's Totient Function to the number of visible lattice points., we have
\begin{equation} \varphi(n) = V_n \end{equation}
and substituting gives
\begin{equation} \mathbb{E}[\varphi(n)] \approx \frac{6n}{\pi^2} \end{equation}
Question
Is it accurate to say the equation
\begin{equation} \mathbb{E}[\varphi(n)] \approx \frac{6n}{\pi^2} \end{equation}
indicates that, on average, the Euler Totient function $\varphi(n)$ approximates $\frac{6n}{\pi^2}$?
