1. **State the problem:** We need to find the derivative of the function $$y = \sin^2(\text{piet} - 2)$$ with respect to the variable inside the sine function. 2. **Rewrite the function:** The function can be written as $$y = (\sin(\text{piet} - 2))^2$$. 3. **Use the chain rule:** The derivative of $$y = [f(x)]^2$$ is $$\frac{dy}{dx} = 2 f(x) \cdot f'(x)$$. 4. **Identify inner function:** Here, $$f(x) = \sin(\text{piet} - 2)$$. 5. **Derivative of inner function:** The derivative of $$\sin(u)$$ with respect to $$u$$ is $$\cos(u)$$. So, $$f'(x) = \cos(\text{piet} - 2) \cdot \frac{d}{dx}(\text{piet} - 2)$$. 6. **Derivative of $$\text{piet} - 2$$:** Assuming $$\text{piet}$$ is a variable, $$\frac{d}{d(\text{piet})}(\text{piet} - 2) = 1$$. 7. **Combine all:** Therefore, $$\frac{dy}{d(\text{piet})} = 2 \sin(\text{piet} - 2) \cdot \cos(\text{piet} - 2) \cdot 1 = 2 \sin(\text{piet} - 2) \cos(\text{piet} - 2)$$. 8. **Simplify using double-angle identity:** Recall that $$\sin(2x) = 2 \sin x \cos x$$, so $$\frac{dy}{d(\text{piet})} = \sin(2(\text{piet} - 2)) = \sin(2\text{piet} - 4)$$. **Final answer:** $$\boxed{\frac{dy}{d(\text{piet})} = \sin(2\text{piet} - 4)}$$