To install <http://fly.io|fly.io> on macOS using Homebrew and authenticate with flyctl, you can follow these steps:

1. Open a terminal on your macOS machine.

2. Install Homebrew if you haven't already. Run the following command in the terminal: /bin/bash -c "$(curl -fsSL <https://raw.githubusercontent.com/Homebrew/install/HEAD/install.sh>)"

3. Once Homebrew is installed, you can use it to install flyctl. Run the following command in the terminal: brew install superfly/tap/flyctl

4. After the installation is complete, you can authenticate with flyctl using the auth login command. Run the following command in the terminal: flyctl auth login

This will open a browser window where you can log in with your <http://fly.io|fly.io> account credentials. Once you log in, the authentication token will be saved on your machine.

5. After successful authentication, you can start using flyctl commands to manage your <http://fly.io|fly.io> resources.

That's it! You have now installed <http://fly.io|fly.io> on your macOS machine using Homebrew and authenticated with flyctl.