The value of $$\tan^2 48^\circ - \cosec^2 42^\circ + \cosec(67^\circ + \theta) - \sec(23^\circ - \theta)$$is:

$$\tan^2 48^\circ - \cosec^2 42^\circ + \cosec(67^\circ + \theta) - \sec(23^\circ - \theta)$$

Now, we know that $$\cosec(90-\theta)=\sec\theta$$

So,$$\tan^2 48^\circ - \sec^2 (90^\circ-42^\circ) + \cosec(67^\circ + \theta) - \sec(23^\circ - \theta)$$

$$\Rightarrow \tan^2 (48^\circ) - \sec^2 (48^\circ) + \cosec(67^\circ + \theta) - \cosec(90^\circ-(23^\circ - \theta))$$

$$\Rightarrow \tan^2 (48^\circ) - \sec^2 (48^\circ) + \cosec(67^\circ + \theta) - \cosec(67^\circ - \theta)$$

$$\Rightarrow -1$$