If you are on version 9 you could use the built-in functions (previously available in the VectorAnalysis
package). The following might get you close to what you need :
Laplacian[f[theta], {r, theta, phi}, "Spherical"] // Simplify
(* (Cot[theta] Derivative[1][f][theta] + (f^\[Prime]\[Prime])[theta])/r^2 *)