content area top Part 1 Show that the function r left parenthesis theta right parenthesis equals theta plus sine squared left parenthesis StartFraction theta Over 3 EndFraction right parenthesis minus 8 has exactly one zero in the interval left parenthesis negative infinity comma infinity right parenthesis. Question content area bottom Part 1 Rolle's Theorem states that for a function f(x) that is continuous at every point over the closed interval left bracket a comma b right bracket and differentiable at every point of its interior left parenthesis a comma b right parenthesis, if f(a)equalsf(b), then there is at least one number c in left parenthesis a comma b right parenthesis at which f prime left parenthesis c right parenthesis equals 0. Part 2 Find the derivative of r left parenthesis theta right parenthesis equals theta plus sine squared left parenthesis StartFraction theta Over 3 EndFraction right parenthesis minus 8