for the basic angle of sinx = +/- sqrt 1/2, all ASTC are supposed to be considered or is it only A and S?
why is 3pi/4 not rejected tho as the range is 0 how do we know that the special angle for sin3pi/4 is 1/sqrt 2

In this particular question, the curve is defined for values of x from 0 to pi, so we only have to consider the first two quadrants.

3pi/4 radians, or equivalently 135 degrees, have a basic angle of pi/4, or equivalently 45 degrees. Clearly the sine of an angle in the second quadrant has a positive value. So, the sine of 3pi/4 has the same signage and value as the sine of pi/4.

From here, the angle 3pi/4 must follow the basic angle pi/4 in computing the value 1 / sqrt 2.

sin pi/4 = 1 / sqrt 2 (or sqrt 2 / 2)

3pi/4 is an angle in the second quadrant with basic value pi/4, so

sin 3pi/4
= sin pi/4
= 1 / sqrt 2