\(\lim\limits_{\theta \to0}\cfrac{1-cos\,4\theta}{1 - cos\,6\theta} \)
\(\lim\limits_{\theta \to0}\cfrac{1-cos\,4\theta}{1 - cos\,6\theta} \) = \(\lim\limits_{\theta \to0}\cfrac{2\,sin^2\,2\theta}{2\,sin^2\,3\theta}\)
Hence, \(\lim\limits_{\theta \to0}\cfrac{1-cos\,4\theta}{1 - cos\,6\theta}=\cfrac49\)