If $|\overrightarrow a|=|\overrightarrow b|=1$ and $|\overrightarrow a+\overrightarrow b|=\sqrt 3$ and $\overrightarrow c$ is such that $\overrightarrow c-\overrightarrow a-2\overrightarrow b=3(\overrightarrow a\times\overrightarrow b)$, then $\overrightarrow c.\overrightarrow b=?$

Question

$\begin{array}{1 1} \frac{-1}{2} \\ \frac{1}{2} \\ \frac{3}{2} \\ \frac{5}{2}\end{array}$