Normalise the parameterised distribution before transforming variance

The probability function of X is

$$P(X=x)=\begin{cases}(2x-1)\theta,&x=1,2,3,\\k,&x=4,\\0,&\text{otherwise},\end{cases}$$

where $0<\theta<1/9$.

(i) Show that $k=1-9\theta$. Find the distribution of X in terms of θ.

(ii) Find $E(X)$ in terms of θ and hence show that $\operatorname{Var}(X)=26\theta-196\theta^2$.

(iii) $Y=a+bX$, with a,b non-zero constants. Given $\operatorname{Var}(Y)=b^2/3$, find θ.