I have to find $\tau$ by finding the gradient of $U(\theta_1, \theta_2, \theta_3)$, where my coordinates are $(\theta_1, \theta_2, \theta_3)$. I assume the gradient is not the simple Cartesian coordinates formula. However, using the spherical or cylindrical coordinates formula seems wrong since my coordinates are three angles and not an angle and a radius. So how do I express $\nabla U$ in this $\theta_1$, $\theta_2$, $\theta_3$ coordinate system? Is there a Jacobian I need, or some other way?
Edit - To make this question clearer, is there a way to express the $\nabla$ operator in a roll-pitch-yaw $\theta_1, \theta_2, \theta_3$ coordinate space? Analogous to how in Cartesian coordinates $\nabla = \frac{\partial}{\partial x} e_x + \frac{\partial}{\partial y} e_y + \frac{\partial}{\partial z} e_z$. I know that the general way to do something like this is via the Jacobian matrix arising from the metric, but am unsure how to do it in this three angle space.