Let $$f(x) = \lim_{\theta \to 0}\left(\frac{\cos\pi x - x^{\frac{2}{\theta}} \sin(x - 1)}{1 + x^{\left(\frac{2}{\theta}\right)} (x - 1)}\right), \quad x \in \mathbb{R}$$. Consider the following two statements :

(I) $$f(x)$$ is discontinuous at $$x=1$$.
(II) $$f(x)$$ is continuous at $$x= - 1$$.
Then,

A

Neither (I) nor (II) is True

B

Only (II) is True

C

Both (I) and (II) are True

D

Only (I) is True