(i) To find the first three terms of \((1 - px)^6\), use the binomial expansion formula:

\((1 - px)^6 = \sum_{k=0}^{6} \binom{6}{k} (-px)^k\).

The first three terms are:

\(\binom{6}{0}(1)^6 = 1\)

\(\binom{6}{1}(-px) = -6px\)

\(\binom{6}{2}(-px)^2 = 15p^2x^2\)

Thus, the first three terms are \(1 - 6px + 15p^2x^2\).

(ii) The expansion of \((1 - x)(1 - px)^6\) involves multiplying \((1 - x)\) by the expansion of \((1 - px)^6\). The coefficient of \(x^2\) is given by:

\(-6p \times (-x) + 15p^2x^2 \times 1 = 0\)

\(15p^2 - 6p = 0\)

Factor the quadratic equation:

\(3p(5p + 2) = 0\)

Thus, \(p = 0\) or \(p = -\frac{2}{5}\).

Since \(p\) is non-zero, \(p = -\frac{2}{5}\).