3. Use the substitution $x=\tan \theta$ to show that $\int \frac{1-x^{2}} {\left(1+x^{2} ight)^{2}} d x=\int \cos 2 \theta d \theta$. [6] Hence find $\int_{0}^{1} \frac{1-x^{2}}{\left(1+x^{2} ight)^{2}} d x$. [4] NB: $\cos ^{2} \theta-\sin ^{2} \theta=\cos 2 \theta$ CS. JG. 123