Given alpha=pi/13=>13alpha=pi
Let
P=prod_(r=1)^6 cos(ralpha)
=>P sinalpha=1/2*2sinalphacosalphaprod_(r=2)^6 cos(ralpha)
=1/4*2sin2alphacos2alphaprod_(r=3)^6 cos(ralpha)
=1/8*2sin4alphacos4alpha*cos3alpha *cos5alpha*cos6alpha
=1/8*sin8alpha*cos3alpha *cos5alpha*cos6alpha
=1/8*sin(13alpha-5alpha)*cos3alpha *cos5alpha*cos6alpha
=1/8*sin(pi-5alpha)*cos3alpha *cos5alpha*cos6alpha
=1/16*2sin5alphacos5alpha *cos3alpha*cos6alpha
=1/16*2sin5alphacos5alpha *cos3alpha*cos6alpha
=1/16sin10alpha *cos3alpha*cos6alpha
=1/16sin(13alpha -3alpha)cos3alpha*cos6alpha
=1/32*2sin(pi -3alpha)cos3alpha*cos6alpha
=1/32*2sin 3alphacos3alpha*cos6alpha
=1/64*2sin 6alphacos6alpha
=1/64*sin 12alpha
=>P sinalpha=1/64*sin (13alpha-alpha)
=>P sinalpha=1/64*sin (pi-alpha)
=>P sinalpha=1/64*sin alpha
=>P=1/64