Maths problem, thanks?

sin² x – 2 sinx cosx – cos² x = 0
sin² x – 2 sinx cosx + cos² x -2 cos² x = 0
(sin x – cos x)² -2 cos² x = 0
(sin x – cos x)² - (√2 cos x)² = 0
(sin x – cos x +√2cos x ) (sin x – cos x - √2cos x ) = 0
[sin x – (1-√2)cos x] [sin x - (1+√2)cos x] = 0
sin x – (1-√2)cos x = 0 or sin x - (1+√2)cos x = 0
sin x = (1-√2)cos x or sin x = (1+√2)cos x
sin x / cos x = 1-√2 or sin x / cos x = 1+√2
tan x = 1-√2 or tan x =1+√2
tan x = -0.4142 or tan x = 2.4142
x = (180-22.5)⁰, (360-22.5)⁰, 67.5⁰, (180+67.5)⁰ , where 0⁰≦x＜360⁰
∴ x = 157.5⁰ , 337.5⁰ , 67.5⁰ , 247.5⁰