In your notebook your variable eta (I am writing it out in latin letters here but you are using the greet eta) does not need to be unprotected. It was never protected.
However, you will note that what appears to be the symbol eta in your notebook is actually not symbol: it is a hyperlink to the documentation for eta. This is why you are getting your various error messages. Enter an eta either by typing
\[Eta]
or by typing any of the keyboard combinations described here:
http://reference.wolfram.com/language/ref/character/Eta.html
