If \[\forall n \in N\] and n>1 ,find the value of \[\lim_{n \to \frac{\pi}{2}} \lfloor \frac{2(sinx-sin^{n}x)+|sinx-sin^{n}x|}{2(sinx-sin^{n}x)-|sinx-sin^{n}x|} \rfloor \] where \[\lfloor . \rfloor \] denotes the greatest integer function.

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