1. **State the problem:** Simplify the expression $$(1 - \sin x\theta)(1 - \sin x\theta)$$. 2. **Formula used:** When multiplying two identical binomials, use the formula for the square of a binomial: $$(a - b)^2 = a^2 - 2ab + b^2$$. 3. **Apply the formula:** Here, $a = 1$ and $b = \sin x\theta$, so $$ (1 - \sin x\theta)^2 = 1^2 - 2 \cdot 1 \cdot \sin x\theta + (\sin x\theta)^2 $$ 4. **Simplify:** $$ = 1 - 2\sin x\theta + \sin^2 x\theta $$ 5. **Final answer:** $$ (1 - \sin x\theta)^2 = 1 - 2\sin x\theta + \sin^2 x\theta $$ This is the expanded and simplified form of the given expression.