(sin(x) + cos(x))^2 = 1/2

sin^2(x) + 2sin(x)cos(x) + cos^2(x) = 1/2

1 + 2sin(x)cos(x) = 1/2

2sin(x)cos(x) = -1/2

sin(2x) = -1/2

2x = 7π/6 + 2πn, 11π/6 + 2πn

x = 7π/12 + πn, 11π/12 + πn