Consider the cubic function f(x) with the leading coefficient being positive, and the function g(x) = e^(sin πx) - 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.





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