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Given the equation:

\[
\csc^4\theta - \cot^4\theta = x^2
\]

We are asked to find the value of:

\[
\frac{2 - \sin^2\theta}{\sin^2\theta}
\]

in terms of \(x\).

### Step 1: Express the given equation in terms of \(\sin\theta\) and \(\cos\theta\)

We know:

\[
\csc\theta = \frac{1}{\sin\theta} \quad \text{and} \quad \cot\theta = \frac{\cos\theta}{\sin\theta}
\]

Thus:

\[
\csc^4\theta - \cot^4\theta = \frac{1}{\sin^4\theta} - \frac{\cos^4\theta}{\sin^4\theta}
\]

This simplifies to:

\[
\csc^4\theta - \cot^4\theta = \frac{1 - \cos^4\theta}{\sin^4\theta}
\]

Using the identity \(1 - \cos^4\theta = (1 - \cos^2\theta)(1 + \cos^2\theta)\), we get:

\[
\csc^4\theta - \cot^4\theta = \frac{\sin^2\theta(1 + \cos^2\theta)}{\sin^4\theta} = \frac{1 + \cos^2\theta}{\sin^2\theta}
\]

So,

\[
x^2 = \frac{1 + \cos^2\theta}{\sin^2\theta}
\]

### Step 2: Simplify the expression \(\frac{2 - \sin^2\theta}{\sin^2\theta}\)

The expression can be rewritten as:

\[
\frac{2}{\sin^2\theta} - 1
\]

Using the identity \(\cos^2\theta = 1 - \sin^2\theta\), we relate this to the earlier equation:

\[
x^2 = \frac{1 + \cos^2\theta}{\sin^2\theta} = \frac{1 + (1 - \sin^2\theta)}{\sin^2\theta} = \frac{2 - \sin^2\theta}{\sin^2\theta}
\]

Thus:

\[
\frac{2 - \sin^2\theta}{\sin^2\theta} = x^2
\]

### Final Answer

The value of \(\frac{2 - \sin^2\theta}{\sin^2\theta}\) in terms of \(x\) is:

\[
\boxed{x^2}
\]

If you have further questions or need additional explanations, feel free to ask!

Here are some related questions:

1. How can you derive trigonometric identities from the Pythagorean identity?
2. What are some other useful trigonometric identities for solving equations?
3. How can you express \(\csc^4\theta\) and \(\cot^4\theta\) in terms of basic trigonometric functions?
4. How can this approach be applied to more complex trigonometric equations?
5. What is the geometric interpretation of the given equation?

**Tip:** When solving trigonometric equations, always check if you can express complex expressions in terms of basic trigonometric identities.

Explore how to find the value of (2 - sin^2(theta)) / sin^2(theta) in terms of x through trigonometric identities and equations. This problem delves into trigonometric concepts, including identities and their applications. Suitable for advanced high school students (Grades 11-12).

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