my question asked me to prove that $\displaystyle \cos 3\theta= 4\cos^3\theta - 3\cos\theta$

i proved already and then the next part asked me to substitute $\displaystyle x=6\cos\theta$ to find the roots of the eqn $\displaystyle x^3 - 27x + 8=0$

i dont know what is point of substituting it. i thought i can just find the roots by keying the eqn into my calculator. can people pls teach me how to find the roots of the eqn without using the calculator?