If vectors $\overrightarrow {a}$ and $\overrightarrow {b}$ are such that $|\overrightarrow {a}| = \large\frac{1}{2}$, $|\overrightarrow {b}| = \large\frac{4}{\sqrt 3}$ and $|\overrightarrow {a} \times \overrightarrow {b}| = \large\frac{1}{\sqrt 3}$ then find $|\overrightarrow {a}. \overrightarrow {b}|$

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