any information about UMVUE of $θ$ in $0<θ<1,P(x=−1)=θ,P(x∈\{0,1,2,3,⋯\})=(1−θ)^{2}θ^{x} $

Question

I was in class and our professor talked about UMVUEs and said this problem is open. I searched for books and papers about this problem but I could not find anything. I search for it in "Theory of Point Estimation E.L. Lehmann" but there was not any useful data.

I searched and find this paper, On the Nile Problem by Sir Ronald Fisher, which seems related. can you help me with references?