Let $$f(x) = x^2$$ and $$g(x) = \sin x$$ for all $$x \in R$$. Then the set of all x satisfying $$(f\circ g \circ g \circ f)(x) = (g\circ g \circ f)(x)$$, where $$(f \circ g)(x) = f(g(x))$$, is

A

$$\pm \sqrt{n \pi}, n \in \left\{0, 1, 2, ....\right\}$$

B

$$\pm \sqrt{n \pi}, n \in \left\{1, 2, ....\right\}$$

C

$$\frac{\pi}{2} + 2n \pi, n \in \left\{....., -2, -1, 0, 1, 2, ....\right\}$$

D

$$2n \pi, n \in \left\{....., -2, -1, 0, 1, 2, ....\right\}$$