Find the value of the expression
![tan\frac{1}{2}[ sin^{-1} \frac{2x}{1+x^{2}}+ cos^{-1} \frac{1-y^{2}}{1+y^{2}} ]](https://tex.z-dn.net/?f=tan%5Cfrac%7B1%7D%7B2%7D%5B+sin%5E%7B-1%7D+%5Cfrac%7B2x%7D%7B1%2Bx%5E%7B2%7D%7D%2B+cos%5E%7B-1%7D+%5Cfrac%7B1-y%5E%7B2%7D%7D%7B1%2By%5E%7B2%7D%7D+%5D "tan\frac{1}{2}[ sin^{-1} \frac{2x}{1+x^{2}}+ cos^{-1} \frac{1-y^{2}}{1+y^{2}} ]")
where |x| < 0 and y > 0 such that xy < 1
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