Let \(f\) be a function holomorphic in \(\mathbb C-\{0,2\}\). Assume that:
(i) \(0\) and \(2\) are first order poles of \(f\);
(ii) that \(f\) is bounded for \(|z|\ge R\) for sufficiently large \(R\);
(iii) the integral \(\int _\gamma f(z)\,dz\) is equal to:
a) \(2\pi i\) if \(\gamma \) is a positively oriented circle of radius \(1\) centered at \(0\);
b) \(0\) if \(\gamma \) is a positively oriented circle of radius \(3\) centered at \(0\).
Determine the function \(f\).