1. **State the problem:** Simplify the expression $$2 - \left[1 - \left(\frac{1}{2} \times \frac{2}{3} \div 1\right)\right] \times (-0.75)^2$$. 2. **Recall the order of operations:** Parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). 3. **Simplify inside the innermost parentheses:** $$\frac{1}{2} \times \frac{2}{3} = \frac{1 \times 2}{2 \times 3} = \frac{2}{6} = \frac{1}{3}$$ 4. **Divide by 1:** $$\frac{1}{3} \div 1 = \frac{1}{3}$$ 5. **Simplify inside the brackets:** $$1 - \frac{1}{3} = \frac{3}{3} - \frac{1}{3} = \frac{2}{3}$$ 6. **Calculate the square of -0.75:** $$(-0.75)^2 = 0.75^2 = 0.5625$$ 7. **Multiply the bracket result by the squared term:** $$\frac{2}{3} \times 0.5625 = \frac{2}{3} \times \frac{9}{16} = \frac{18}{48} = \frac{3}{8} = 0.375$$ 8. **Subtract from 2:** $$2 - 0.375 = 1.625$$ **Final answer:** $$1.625$$