PUMaC 2010 Team Sudoku Problem 4

Across Macky found two angles a and b, and the two relations

\cos a+\cos b=5 \sqrt{\frac{2}{29}} \quad \sin a+\sin b=\frac{4}{\sqrt{29}}

Given these two pieces of information, Macky wants to find the value of \cos (a-b), which to his surprise turns out to be a positive rational number, i.e. a positive fraction of the form m / n, for integers m and n with n \neq 0. He reduces this fraction to its lowest form and concatenates the numerator and the denominator together. What is the final result he obtains?