Question 757630
{{{cos(3*theta) = cos(theta+2*theta) = cos(theta)*cos(2*theta)-sin(theta)*sin(2*theta)}}}

{{{cos(2*theta) = (cos(theta))^2-(sin(theta))^2}}}

{{{sin(2*theta) = 2 sin(theta) cos(theta)}}}

Replacing lines 2 and 3 into the first one and a bit of algebra:

{{{cos(3*theta) = (cos(theta))^3-3 cos(theta) (sin(theta))^2}}}

If you want only cosine functions replace {{{(sin(theta))^2 = 1-(cos(theta))^2}}}:

{{{cos(3*theta) = 4 (cos(theta))^3 - 3 cos(theta)}}}