Consider the cubic function \( f(x) \) with the leading coefficient being positive, and the function \( g(x) = e^{\lambda (\sin \pi x)} - 1 \), both defined over the set of all real numbers. The composite function \( h(x) = g(f(x)) \) satisfies the following conditions:

(a) The function \( h(x) \) has a local maximum value of 0 at \( x = 0 \).

(b) In the open interval \( (0,3) \), the equation \( h(x) = 1 \) has seven distinct real roots.

Given \( f(3) = 1/2 \) and \( f'(3) = 0 \), find the value of \( p + q \) when \( f(2) = q/p \). Here, \( p \) and \( q \) are coprime natural numbers.