Verified answer

Sin⁡ 4 x = -√2 /2

sin 4x = (-1/2) sqrt (2)

The sine is negative in the 3rd and 4th quadrants (pi, 3pi/2) and (3pi/2,2pi).

sin 4x = -0.5 (1.414) = 0.707

arcsin 4x = 45 degrees

4x = 45 degrees, but that's in the third quadrant so add 180 to it = 225

x = 225/4 = 56.25

same method in 4th quadrant.