\dfrac{1}{\Theta\Phi} \left[ \dfrac{\partial^2}{\partial\phi^2} (\Theta\Phi) + \sin\theta \dfrac{\partial}{\partial\theta} \left( \sin\theta \dfrac{\partial}{\partial\theta}\right) (\Theta\Phi) = -\lambda \sin^2\theta (\Theta\Phi) \right] \dfrac{1}{\Theta\Phi}