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The article below may be able to help you with this issue.
Click on the link below to see more details and screenshots.
I've quoted some helpful highlights for you:
... Reset your Apple TV by unplugging it from the power source for thirty seconds.
Also, see if the issue persists if you try to login to Netflix from your iPad or computer.
I hope this information helps ....
Have a great day!
This happened to me too. In the end I deduced that it was because I was using the same e-mail address that I had used years ago for my long dormant Netflix account. When I tried with a different e-mail address it worked perfectly and I was able to start the free month with the account linked to my itunes ID.