How I mentally cope with this is:

I get paid regardless of what I'm working on. If management asks me to shift gears (which they do, often) its because that's the most valuable thing for me to do at that time. At the end of the day, my goal is to provide value to the company.

Does it suck. Yes. But its part of my current job.

I've worked at other places where this happens much less often as well, such places do exist.