Hello, can someone help me please?

I have to find the minimum (x,y) over the domain [0;2Pi] of the following function

f(x,y):=1+8 cos(1/2 x-1/2 y) cos(1/2 x) cos(1/2 y) which i plotted to have an idea where its minimum is located.

plot3d(f(x,y),x=0..2Pi,y=0..2Pi)

I tried to use the command  ' minimize(f(x,y)) '

Thank you in advance,

best regards.

 Ps: the function normaly attains its minimum at (2Pi/3,-2Pi/3) and (-2Pi/3,2Pi/3).

Hey any one can help? I calculated the characteristical Polynom of my Matrix M:

-(lambda-2)^2*(544-lambda^9-328*lambda^7-16*cos(x-y)+6*cos(x-y)*lambda+6*cos(x+y)*lambda-408*cos(y)*lambda^2-408*cos(x)*lambda^2+540*cos(y)*lambda+540*cos(x)*lambda-28*cos(y)*lambda^4-28*cos(x)*lambda^4+152*cos(y)*lambda^3+152*cos(x)*lambda^3+2*cos(y)*lambda^5+2*cos(x)*lambda^5-256*cos(y)+17232*lambda^2-256*cos(x)-7852*lambda^5+17768*lambda^4+2088*lambda^6+28*lambda^8-16*cos(x+y)-23632*lambda^3-5844*lambda)

now I want to solve the second part of the polynomial with lambda^9 but maple gives me the RootOf-function

_Z^9-28*_Z^8+328*_Z^7-2088*_Z^6+(-2*cos(y)-2*cos(x)+7852)*_Z^5+(28*cos(y)+28*cos(x)-17768)*_Z^4+(-152*cos(y)-152*cos(x)+23632)*_Z^3+(408*cos(y)+408*cos(x)-17232)*_Z^2+(-12*cos(x)*cos(y)-540*cos(y)-540*cos(x)+5844)*_Z+32*cos(x)*cos(y)+256*cos(y)+256*cos(x)-544

How can I simplify this expression to solve over lambda.

purpose is to plot all the eigenvalues.

Thank you in advance.