Chapter 9.8, Problem 22MP

In spherical coordinates, find the $\theta$ Lagrange equation for a particle moving in the potential field $V=V(r,\theta ,\varphi ).$ What is the $\theta$ component of the acceleration? Hint: The $\theta$ Lagrange equation is the $\theta$ component of $ma=F=-\nabla V;$ for components of $\nabla V,$ see Chapter 6, end of Section 6, or Chapter 10, Section 9.