I found the answer here
Let $X \subset \mathbb{R}^3$ be the union of $n$ lines through the origin. Compute $\pi_1(\mathbb{R}^3 − X)$
My thinking: Deformation retraction of $\mathbb{R}^3-\{0\}$ onto $S^2$ is given by
$f_t:\mathbb{R}^3\setminus\{0\} \to \mathbb{R}^3\setminus\{0\}$ defined by
$f_t(x)= (1-t)x+ t\frac{x}{|x|} $ where $t \in [0,1]$
My question : How do we show that $S^2-\{x_1,x_2,...,x_{2n}\} $ as a deformation retract of $\mathbb{R}^3 -X $ where $x_1,x_2,,....,x_{2n}$ are the $2n$ points in the intersection $X \cap S^2$
finally my question is that how to prove that $S^2-\{x_1,x_2,...,x_{2n}\} $ as a deformation retract of $\mathbb{R}^3 -X ?$