Prove each of the following identities :
`(1+ tan^(2) theta)(1+ cot^(2) theta)=(1)/((sin^(2) theta- sin^(4) theta)) `

Explanation

To prove the identity \((1 + \tan^2 \theta)(1 + \cot^2 \theta) = \frac{1}{\sin^2 \theta - \sin^4 \theta}\), we will start with the left-hand side (LHS) and simplify it step by step.

### Step 1: Write down the left-hand side
\[ \text{LHS} = (1 + \tan^2 \theta)(1 + \cot^2 \theta) \]

### Step 2: Use the Pythagorean identities
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