I only zone out in meetings with no focus. Provide an agenda which describes what you want to talk about. This helps me identify my value and not begin to immediately wonder how long this aimless meeting will last. Describe the problem this meeting wants to solve and why you can't solve it by yourself. People schedule meetings and expect attendees to do the work on making the meeting successful.
It's not my responsibility not to be bored, it's the organizers responsibility to be engaging.