Limit.

[man111]

Suppose $x_{1}=tan^{-1}2>x_{2}>x_{3}.........$ are positive real no. satisfying $\displaystyle sin(x_{n+1}-x_{n})+2^{-(n+1)}sinx_{n}sin_{n+1}=0\forall n\geq 1.$ Then the value of $tan(\displaystyle\lim_{n\to\infty}x_{n})$ is

[zhoraster]

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