Existence of a smooth path connecting two points Let $U=\{(x,y)\in \mathbb{R}^2 | 1<x^2+y^2<4\}$. Let $p,q\in U$. Show that there is a continuous map $\gamma : [0,1] \to U$ such that $\gamma (1)=q$ and $\gamma (0)=p$ and such that $\gamma$ is differentiable on $(0,1)$

I really don't know how think this problem $\gamma $ is a continuous function and given that $\gamma (1)=q$  and $\gamma (0)=p$ then how construct $\gamma $ is differentiable on $(0,1)$? Any help plzzz..

Hint
Identify $\mathbb{R}^2$ with the complex plane $\mathbb{C}.$ Write $p=r_1 e^{i\theta_1}$ and $q=r_2 e^{i\theta_2}$. 
Consider 
$$\gamma(t)=(tr_1+(1-t)r_2)e^{i(t\theta_1+(1-\theta_2)}.$$
