cos(5[pi]/24)+cos([pi]/24)

i have to find the exact value of that.

so I simplified cos(5pi/24) to cos(pi/3 - pi/8) and then used a difference formula for cos to get

(sqrt2/2){[sqrt2+(sqrt2)]} + (sqrt3/2){[sqrt2-(sqrt2)]}

did the same thing for cos(pi/24) and got

(sqrt3/2){[sqrt2+(sqrt2)]} + (1/2){[sqrt2+(sqrt2)]}

so where do i go from there? How do I add these huge squarerooted expressions together to find the exact value? Please help. I'm running out of time and getting frustrated! Thank you!