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.