Nikon is expanding its list of D750 bodies affected by a shutter issue that may cause shading across a captured image. This is expansion follows a similar one in February 2016, which followed the original notice back in July 2015. The ranges of dates of manufacture of the cameras with this issue vary sporadically and include bodies produced from the start all the way through as recently as September of last year, so it's best to check your serial number (my personal body is affected).
You can put your serial number into a form on Nikon's site (scroll down a ways) to see if you should seek repairs at your local Nikon service center (my body is actually affected now, too). Thankfully, I have a service center relatively close to me here in Los Angeles, but others will certainly not be so lucky.
Hopefully, you can get your body fixed as soon as possible if you do have the shutter problem. Nikon will repair bodies even if out of warranty, of course, since this is an issue with a faulty part and is not standard wear and tear.
If you've been experiencing this issue, how bad is it? Do you have photos that repeatedly feature this shading? Let us know.
Update: In a phone call, a Nikon representative stated it should take 7-10 days to fix the problem, but that faster service could be requested, but not guaranteed. NPS members can receive service in 5-7 business days. In both cases, Nikon provides a mailing label so you can ship your camera free-of-charge (you'll still have to find a box, though).