In a circle, parallel chords of lengths 2,3,4 determine central angles \(\alpha ,\beta ,\alpha +\beta \) radians, respectively, where \(\alpha +\beta <\pi \), If \(\cos \alpha \), Which is a positive rational numbers, is expressed as a fraction in lowest terms, what is the sum of its numerator and denominator?

(第三届AIME1985 第9题)