Struggling! Need help with Trig please! Find real zeros

Find the real zeros of the trigonometric function on the interval 0 less than or equal to x less than 2pi

f(x)=sin(2x) +sqrt(2)cos x

0 = 2sinxcosx + sqrt(2)cosx

0 = cosx(2sinx + sqrt(2))

cosx = 0 or 2sinx + sqrt(2) = 0

x = pi/2 or 3pi/2 and x = 5pi/4 or 7pi/4