For the function $$f(x) = \sin x + 3x - \frac{2}{\pi}(x^2 + x)$$, where $$x \in [0, \frac{\pi}{2}]$$, consider the following two statements : (I) $$f$$ is increasing in $$(0, \frac{\pi}{2})$$. (II) $$f'$$ is decreasing in $$(0, \frac{\pi}{2})$$. Between the above two statements,

$$f(x) = \sin x + 3x - \frac{2}{\pi}(x^2 + x)$$ on $$[0, \pi/2]$$.

Statement (I): f is increasing in $$(0, \pi/2)$$.

At $$x = 0$$: $$f'(0) = 1 + 3 - 0 - 2/\pi = 4 - 2/\pi > 0$$.

At $$x = \pi/2$$: $$f'(\pi/2) = 0 + 3 - 2 - 2/\pi = 1 - 2/\pi \approx 1 - 0.637 = 0.363 > 0$$.

Statement (II): f' is decreasing in $$(0, \pi/2)$$.

Since $$\sin x \geq 0$$ for $$x \in (0, \pi/2)$$: $$f''(x) = -\sin x - 4/\pi < 0$$ for all $$x$$ in this interval.

So $$f'$$ is indeed decreasing. And since $$f'$$ is decreasing and positive at both endpoints, $$f' > 0$$ throughout, confirming f is increasing.

Both statements are true.

The correct answer is Option (4): both (I) and (II) are true.