Write each expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression and all functions are of $\theta$ only. \[ \frac{\csc ^{2}(-\theta)-1}{1-\cos ^{2}(-\theta)} \] \[ \frac{\csc ^{2}(-\theta)-1}{1-\cos ^{2}(-\theta)}= \]

Step 1 ：Write each expression in terms of sine and cosine, and then simplify so that no quotients appear in the final expression and all functions are of \(\theta\) only.

Step 2 ：Given expression: \[\frac{\csc ^{2}(-\theta)-1}{1-\cos ^{2}(-\theta)}\]

Step 3 ：Convert the given expression into terms of sine and cosine. The cosecant function is the reciprocal of the sine function, so \(\csc^2(-\theta)\) can be written as \(\frac{1}{\sin^2(-\theta)}\). The denominator \(1-\cos^2(-\theta)\) is equivalent to \(\sin^2(-\theta)\) by the Pythagorean identity. Therefore, the expression can be simplified to \(\frac{1}{\sin^2(-\theta)} - 1\) divided by \(\sin^2(-\theta)\).

Step 4 ：Simplify the expression to \(\frac{\cos^2(-\theta)}{\sin^4(-\theta)}\). However, this expression still contains a quotient.

Step 5 ：To remove the quotient, we can multiply the numerator and the denominator by \(\sin^4(-\theta)\), which gives \(\cos^2(-\theta)\).

Step 6 ：The final simplified expression with no quotients and all functions of \(\theta\) only is \(\boxed{\cos^2(-\theta)}\).