matrix with sin and cos? help wanted.

Hi guys, this question bothers me...

I have a matrix A=

cos(theta) sin(theta)

-sin(theta) cos(theta)

So it is a 2x2 matrix. I am asked to show that e to the power of (i theta)

and e to the power of (-i theta) are eigenvalues. Then to find eigenvectors and simple formula for A to pwr of n.

Now, I guess I should proceed finding determinant of A(with - lambda from left top to bottom right)=0. However, i can't find my way out of this. I get smth like lambda squared + sin squared theta+ cos squared theta - 2lambda cos theta=0.

Any help is appreciated!