某数学学习小组甲、乙、丙三人分别构建了如图所示的正四棱台(1), (2), (3), 从左往右, 若上底面边长、下底面边长、高均依次递增 $d \mathrm{~cm}$, 记正四棱台(1), (2), (3)的侧棱与底面所成的角分别为 $\alpha_1, \alpha_2, \alpha_3$, 正四棱台(1),(2),(3)的侧面与底面所成的角分别为 $\theta_1, \theta_2, \theta_3$, 则
$\text{A.}$ $\sin \alpha_1+\sin \alpha_3=2 \sin \alpha_2$
$\text{B.}$ $\tan \alpha_1+\tan \alpha_3=2 \tan \alpha_2$
$\text{C.}$ $\cos \theta_1+\cos \theta_3=2 \cos \theta_2$
$\text{D.}$ $\tan \theta_1+\tan \theta_3=2 \tan \theta_2$