At which values in the interval [0, 2π) will the functions f (x) = 2cos2θ and g(x) = −1 + 4cos θ − 2cos2θ intersect?

Elizabeth claims that the fourth root of 2 can be expressed as 2^m since (2^m)^n = 2. find the values of m and n for the case where elizabeth's claim is true.