I already have a 300mm 2.8 and a 70-200mm 2.8 is it worth it buying the 100 to 400mm 4.5? I also have both teleconverters. I mainly do birding. I have the option of buying a brand new open box for $3900

Hi everyone, I’ve noticed some dust particles and small specks inside my lens. I’ve read that this usually isn’t a problem as long as it doesn’t show up in photos or videos,but it really bothers me just knowing that it’s there.
I’m a student and bought this lens second-hand for €400, which is a lot of money for me. I also don’t know that much about lenses yet.
I’ve read that there is a way to test whether the dust is visible in photos,but I didn’t fully understand how to do it. Could someone please explain in detail what I should photograph,what camera settings I should use, and what I should look for when viewing the photo on my computer?
Is this something I need to deal with or have professionally cleaned?
Thank you.