How do you find the solutions of the equation 2sin^2(x)=1

Solve for x:
2 sin^2(x) = 1

Divide both sides by 2:
sin^2(x) = 1/2

Take the square root of both sides:
sin(x) = 1/sqrt(2) or sin(x) = -1/sqrt(2)

Take the inverse sine of both sides:
x = 2 π n_1 + (3 π)/4 for n_1 element Z or x = 2 π n_2 + π/4 for n_2 element Z or sin(x) = -1/sqrt(2)

Take the inverse sine of both sides:
  x = 2 π n_1 + (3 π)/4 for n_1 element Z or x = 2 π n_2 + π/4 for n_2 element Z or x = 2 π n_3 + (5 π)/4 for n_3 element Z or x = 2 π n_4 + (7 π)/4 for n_4 element Z

Where is the problems