Find the period of the function in Exercise 76; that is, in terms of m and n, find the smallest positive real number T such that r(t + T) = r(t) for all t.

Data from Exercise 76

Prove that for integers m and n, the curve

r(t)= (a sin mt cos nt, b sin mt sin nt, c cos mt)

lies on the surface of a sphere provided a² = b² = c².