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The equation in the image seems partially extracted due to text recognition limitations. However, from what I can make out, the given expression is as follows:

\[
\frac{(\sin \theta + \cos \theta)^2 - 3 \sin \theta \cos \theta}{\cos \theta (\sec \theta - \csc \theta)} \cdot \frac{\sin^2 \theta - \cos^2 \theta}{\sin^3 \theta + \cos^3 \theta}
\]

Let me work through this expression to simplify it step by step.

1. **Expression 1 (Numerator)**: 
   \[
   (\sin \theta + \cos \theta)^2 - 3 \sin \theta \cos \theta
   \]
   Expanding the square:
   \[
   (\sin^2 \theta + 2 \sin \theta \cos \theta + \cos^2 \theta) - 3 \sin \theta \cos \theta
   \]
   Since \( \sin^2 \theta + \cos^2 \theta = 1 \), this simplifies to:
   \[
   1 + 2 \sin \theta \cos \theta - 3 \sin \theta \cos \theta = 1 - \sin \theta \cos \theta
   \]

2. **Expression 2 (Denominator)**:
   \[
   \cos \theta (\sec \theta - \csc \theta)
   \]
   We know \( \sec \theta = \frac{1}{\cos \theta} \) and \( \csc \theta = \frac{1}{\sin \theta} \), so:
   \[
   \cos \theta \left( \frac{1}{\cos \theta} - \frac{1}{\sin \theta} \right) = 1 - \frac{\cos \theta}{\sin \theta} = \frac{\sin \theta - \cos \theta}{\sin \theta}
   \]

3. **Expression 3 (Other factors)**: 
   The second part involves:
   \[
   \frac{\sin^2 \theta - \cos^2 \theta}{\sin^3 \theta + \cos^3 \theta}
   \]
   This can be rewritten as a difference of squares and cubes. Let me further simplify this next.

I'll now simplify this whole expression.The given complex expression simplifies to \( \sin \theta \).

If you have further questions about specific steps or need more details, feel free to ask! Here are some related questions to explore:

1. How can trigonometric identities help simplify complex expressions?
2. What is the significance of \(\sin^2 \theta + \cos^2 \theta = 1\) in trigonometry?
3. How do you derive the sum and difference of cubes for trigonometric functions?
4. What are the applications of secant (\(\sec \theta\)) and cosecant (\(\csc \theta\)) identities?
5. Can this technique be applied to other complex trigonometric expressions?

**Tip:** When simplifying trigonometric expressions, always look for opportunities to apply basic identities such as the Pythagorean identity.

Simplify the given trigonometric expression: \( \frac{(\sin \theta + \cos \theta)^2 - 3 \sin \theta \cos \theta}{\cos \theta (\sec \theta - \csc \theta)} \cdot \frac{\sin^2 \theta - \cos^2 \theta}{\sin^3 \theta + \cos^3 \theta} \).

This step-by-step guide simplifies a complex trigonometric expression using identities like \( \sin^2 \theta + \cos^2 \theta = 1 \) and other core trigonometric formulas. Suitable for Grades 11-12 students, it explains the process with detailed breakdowns.

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