In the expansion of \[\frac{1+3x}{(1+ax)^2}\] in ascending powers of \(x\), the coefficient of \(x\) is zero. Find the value of the constant \(a\), and, when \(a\) has this value, obtain the expansion up to and including the term in \(x^3\).

In the expansion of \[\frac{1+3x}{(1+ax)^2}\] in ascending powers of \(x\), the coefficient of \(x\) is zero. Find the value of the constant \(a\), and, when \(a\) has this value, obtain the expansion up to and including the term in \(x^3\).