You are going to need the Task Force Arrowhead Radio (TFAR) in order for the Public Server to let you in. Do not use the Task Force Radio you downloaded through Steam.
If you are launching through Steam (which is how I have been doing it)
-download through this link: https://drive.google.com/file/d/12jEz4Ff1sSL4ltMPxMJ607hDblPdCEgY/view
-Open it and unizip the file onto the ARMA 3 folder through the Programs Files (x86)
-Once downloaded, in the Mods section of ARMA 3 Launcher, use Local Mods button to load TFAR, and the turquoise bar at the bottom will appear saying its downloaded or ready to load.
-Once checked off, make sure the Teamspeak plugin is installed, and then launch and load into the server.
Hope this helps.