sin(theta)-cos(theta)=-root 2

Question

The answer is between 0 < or equal to theta< 2pi

Answer 1

Do square to both sides of equation 

sin^2(theta)-2sin(theta)cos(theta) +cos^2(theta) = 2

1 - 2sin(theta)cos(theta) =2

because sin^2+cos^2 =1

2sincos is formula for double angle,

so you can substitute:

1-sin(2theta) = 2

-sin(2theta) =1

find 2theta , it will be 270 degree and divide by 2 to find theta.