The fundamental group of $SO(3)/SO(2)$

Question

Since the homogeneous space $M:=SO(3,\mathbb R)/SO(2,\mathbb R)$ is diffeomorphic to the sphere then $\pi_1(M)=0$. Now how to show the same for complex orthogonal groups. I mean if $X:=SO(3,\mathbb C)/SO(2,\mathbb C)$ then how to show that $\pi_1(X)=0$?