a question about solving recurrence with constant

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Solve ${x_n}^2sin(\theta)={d^2-\frac{|x_{n-1}-x_{n+1}|}4}^2{} \& x_{n+1}=x_ncos(\theta)\pm \sqrt{{x_n}^2(cos^2(\theta)+1)-d^2}$

--I am really confused about howcan I deal with the constant term. If there is not this constant d then I can solve this easily, but this constant really prevent me from doing most of the things I have learnt. I tried to substitute $x_{n}$ with other variable to neglect this constant term, but my attempts failed. Is there a way to deal with this constant term? Thank you..