Compute \(\displaystyle\int_0^{2\pi} \frac{d\theta}{1 + a\cos\theta}\,\mathrm{d}x\) with \(|a| < 1\);
Erratum: the trailing \(\mathrm{d}x\) is printed in the source after \(d\theta\) and is a typo; the integral is \(\int_0^{2\pi} \frac{d\theta}{1 + a\cos\theta}\) with integration variable \(\theta\) and no \(x\) in the integrand.