Find the orbit space $T^2 / \mathbb Z_2$

Question

Let $T^2$ be the unit torus $$ T^2 = \left\{ (\lambda, \lambda') \in \mathbb C^2 \mid |\lambda| = |\lambda'| = 1 \right\}. $$ Then the group $\mathbb Z_2$ is acting on $T^2$ by the rule $[1]\cdot(\lambda,\lambda') = (-\lambda',-\lambda)$ or in the angle notation $[1](e^{i\varphi},e^{i\psi}) = (e^{i(\psi+\pi)},e^{i(\varphi+\pi)})$. My question is how to find the orbit space $T^2 / \mathbb Z_2$? I tried to represent $T^2$ as a rectangle with sides glued together (it helps to find factorspace $T^2 / \mathbb Z_2$ in the case of action $[1](\lambda,\lambda') = (\lambda',\lambda)$: in this case this is the Möbius strip) but in this case it doesn't help.