Long's answer is the best one for modern Desktops like Gnome, because Gnome itself uses xkb and overwrites xmodmap configurations by default (also, xmodmap is on its way out and unsupported in Wayland). Unfortunately, it will still only work until reboot.
You can apply this option permanently for your Gnome desktop with this command:
gsettings set org.gnome.desktop.input-sources xkb-options "['lv3:caps_switch']"
Of course you can also make this change permanently and even system wide, without using Gnome. If you use Gnome, you should still use the above command to keep Gnome from overwriting this setting. For Arch, you can add a file
/etc/X11/xorg.conf.d/90-custom-kbd.conf with the following content:
Identifier "keyboard defaults"
Option "XKbOptions" "lv3:caps_switch"
I assume this differs between distributions, so your mileage might vary.