(i) To find the coefficient of \(x^2\) in \((1 - 2x)^7\), use the binomial theorem: \(\binom{7}{2}(-2x)^2 = 21 \times 4x^2 = 84x^2\). The coefficient is 84.

For \(x^3\), \(\binom{7}{3}(-2x)^3 = 35 \times (-8x^3) = -280x^3\). The coefficient is -280.

(ii) The coefficient of \(x^3\) in \((2 + 5x)(1 - 2x)^7\) is found by expanding and combining terms: \(2 \times (-280) + 5 \times 84 = -560 + 420 = -140\).