Let [tex] \rm{f(x)=3 \:sin(x)+2.}[/tex] For any
[tex] \rm x_1 \in \bigg[0, \dfrac{\pi}{2} \bigg],[/tex] there exists an [tex] \rm x_2 \in \bigg[0, \dfrac{\pi}{2} \bigg],[/tex] such that [tex] \rm f( \rm x_1) +2 f(\rm x_2 + \theta) = 3[/tex].

Which of these could be the value of [tex]\theta[/tex]?

[tex](1) \: \frac{3\pi}5 \\ \\ (2) \: \frac{4\pi}5 \\ \\ (3) \: \frac{6\pi}5 \\ \\ (4) \: \frac{7\pi}5 [/tex]
​