1. Open TextEdit as sudo

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        sudo -b /Applications/TextEdit.app/Contents/MacOS/TextEdit

2. Open /etc/hosts in this new TextEdit instance using any of the following methods:

   - Append the path to the end of the previous command
   - Use File → Open
   - Drag the file to the sudo'd TextEdit on the Dock

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Alternatively, you can edit in Terminal using nano:

    SUDO_EDITOR=nano sudo -e /etc/hosts

Using `sudo -e` ensures that temporary files etc. are handled in the proper way and you don't run into permission issues with them. `nano` is a simple console-based editor which is quite user-friendly.