macOS – How to Eject a DVD Without Logging In

First of all, try the "nice" way using the drive utility

drutil tray eject

If this doesn´t work (probably because the system can´t unmount the volume), the following command will forcefully unmount the Volume with name "untitled" (make sure you´re using the right mountpoint!!):

hdiutil detach -force /Volumes/untitled

Reboot the computer while holding down the mouse button - if there's no physical issue preventing ejection, the disc will be ejected.

You can of course use terminal to try to force an eject, but this requires a little knowledge of text commands and is covered here:

• Is there a Terminal command that will force open the DVD tray?