The value of $\frac{\tan ^{2} \theta}{1+\tan ^{2} \theta}+\frac{\cot ^{2} \theta}{1+\cot ^{2} \theta}$ is equal to

$\frac{\tan ^{2} \theta}{1+\tan ^{2} \theta}+\frac{\cot ^{2} \theta}{1+\cot ^{2} \theta}$

$=\frac{\tan ^{2} \theta}{\sec ^{2} \theta}+\frac{\cot ^{2} \theta}{\operatorname{cosec}^{2} \theta}$

$=\frac{\sin ^{2} \theta}{\cos ^{2} \theta} \times \cos ^{2} \theta+\frac{\cos ^{2} \theta}{\sin ^{2} \theta} \times \sin ^{2} \theta$

$=\sin ^{2} \theta+\cos ^{2} \theta=1$