Define the quantum mechanical operators for the angular momentum $\hat{\mathbf{L}}$ and the total angular momentum $\hat{L}^{2}$ in terms of the operators $\hat{\mathbf{x}}$ and $\boldsymbol{\nabla}$. Calculate the commutators $\left[\hat{L}_{i}, \hat{L}_{j}\right]$ and $\left[\hat{L}^{2}, \hat{L}_{i}\right]$.