2. The plane $\alpha$ forms angles $\theta_{i}(i=1,2, \cdots, 6)$ with the six faces of a rectangular prism, then the value of $\sum_{i=1}^{6} \sin ^{2} \theta_{i}$ is
A. 2
B. 3
C. 4
D. 6
Consider the normal vector $\overrightarrow{A C_{1}}$ of $\alpha$, and construct a rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$ with faces parallel to the original rectangular prism. Then, the sum of the cosines of the angles formed by $A C_{1}$ and the faces of the rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$ is the required $\sum_{i=1}^{6} \sin ^{2} \theta_{i}$. Since $\cos ^{2} \angle C_{1} A C+\cos ^{2} \angle C_{1} A D_{1}+\cos ^{2} \angle C_{1} A B_{1}$ $=\frac{A C^{2}+A D_{1}^{2}+A B_{1}^{2}}{A C_{1}^{2}}=2 \Rightarrow \sum_{i=1}^{6} \sin ^{2} \theta_{i}=4$. Similarly, it can be verified that the conclusion also holds when $\overrightarrow{A C_{1}}$ is parallel to some faces of the rectangular prism. Therefore, the answer is $C$.