3. Given a unit cube $A B C D-A_{1} B_{1} C_{1} D_{1}$, there are two moving points $E$ and $F$ on the opposite edges $B B_{1}$ and $D D_{1}$, respectively, such that $B E=D_{1} F$. Let the angle between $E F$ and the plane $A B$ be $\alpha$, and the angle between $E F$ and the plane $B C_{1}$ be $\beta$. Then the maximum value of $\alpha + \beta$ is ( ).
A. $120^{\circ}$
B. $90^{\circ}$
C. $60^{\circ}$
D. Does not exist
3. B By symmetry, we know that $\alpha=\beta$, and $\sin \alpha=\frac{1}{E F} \leqslant \frac{1}{\sqrt{2}}$, so $\alpha \leqslant 45^{\circ}, \alpha+\beta \leqslant 90^{\circ}$.