Solve equation on the interval 0 to 2pi Sqrt2cos^2+cos=0?

√2 cos²θ + cosθ = 0
cosθ (√2 cosθ + 1) = 0
cosθ = 0 or √2 cosθ + 1 = 0
cosθ = 0 or cosθ = -1/√2
θ = π/2, 3π/2 or θ = π - (π/4), π + (π/4)
θ = π/2, 3π/4, 5π/4, 3π/2

sqrt(2) cos^2 x + cos x = 0
cos x( sqrt(2) cos x + 1) = 0
cos x = 0
x = pi/2, 3pi/2

sqrt(2) cos x + 1 = 0
sqrt(2) cos x = -1
cos x = -1/sqrt(2)
x = 3pi/4, 5pi/4

x= pi/2, 3pi/2, 3pi/4, 5pi/4