Mean of a discrete pmf with unknown constants

Let $X$ be a discrete random variable with the probability mass function

$$P(X=n)=\begin{cases}\dfrac{-2c}{n}, & n=-1,-2,\ d, & n=0,\ cn, & n=1,2,\ 0, & \text{otherwise,}\end{cases}$$

where $c$ and $d$ are positive real numbers. If $P(|X|\le1)=3/4$, then $E(X)$ equals