Note: z = cis(@) here.

I worked out that

z + z^-1 = 2cos(@) ---1

(z + z^-1)^3 = z^3 + z^-3 + 3(z+z^-1) --- 2

Now I need to prove cos(3@) = 4cos^3(@) - 3cos(@)

I try to sub in 2cos(@) into 2 for (z + z^-1), and fiddle around, but am unable to prove the above.

Any suggestions? Thanks.