real analysis

Suppose $x_1$ = ${tan^{-1}}2$$\geq x_1$$\geq x_2$…………………….. are positive real numbers satisfying
sin($x_{n+1}- x_n ) + 2^{-(n+1)}sin x_n sin x _{n+1}$ = 0 for all $ n\geq1$ .
Find $cot x _ n$.
Also show that $\displaystyle\lim_{n\to\infty}$$x_n$ = $\frac{\pi}{4}$.

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