What is the value of tan2 θ−sec2 θcot2 θ−cosec2 θ.

We have,

$\frac{\tan ^{2} \theta-\sec ^{2} \theta}{\cot ^{2} \theta-\operatorname{cosec}^{2} \theta}=\frac{-1\left(\sec ^{2} \theta-\tan ^{2} \theta\right)}{-1\left(\operatorname{cosec}^{2} \theta-\cot ^{2} \theta\right)}$

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

We know that,

$\sec ^{2} \theta-\tan ^{2} \theta=1$

$\operatorname{cosec}^{2} \theta-\cot ^{2} \theta=1$

Therefore,

$\frac{\tan ^{2} \theta-\sec ^{2} \theta}{\cot ^{2} \theta-\operatorname{cosec}^{2} \theta}=\frac{1}{1}$

$=1$