solve sin (pi/4(x-6))=0.5 algebraically

If we just restrict ourselves to [0, 2pi], the sine will equal .5 at  pi/6 and 5p/6 rads

So we have....   (pi/4(x-6))= pi/6  →  pi/4 *x - 3pi/2  = pi/6  →    pi/4 * x  =  [5pi/3]/   →  x = [5pi/3][4/pi]

→  20/3

Also ....   (pi/4(x-6)) = 5pi/6 →  pi/4 *x - 3pi/2  = 5pi/6  → pi/4 * x = [7 pi/3] →  x = [7pi/3][4/pi]  →  28/3

what about domain 0<x<2pi??

$$\begin{array}{rlll} sin (\frac{\pi(x-6)}{4})&=&0.5\\\\ \frac{\pi(x-6)}{4}&=&n\pi +(-1)^n\times \frac{\pi}{6}\qquad & n\in Z\\\\ x-6&=&4n +(-1)^n\times \frac{4}{6}\qquad & n\in Z\\\\ x&=&4n+6 +(-1)^n\times \frac{2}{3}\qquad & n\in Z\\\\ x&=&4n+6 + \frac{(-1)^n\times 2}{3}\qquad & n\in Z\\\\ \end{array}$$

I guess that is the domain since that is all the values that x can be  :/

thank you so much guys, i really appreciate it