Given the functions

$\displaystyle f(x) = \exp(\arccos \left(\sin \left(x + \frac{\pi}{3}\right)\right))$,

$\displaystyle g(x) = \mbox{arccsc} \left(\frac{4 - 2\cos x}{3}\right)$

and the function $\displaystyle h(x) = f(x)$ defined only for the common domain of $\displaystyle f(x)\ \mbox{\&}\ g(x)$.

Calculate range of $\displaystyle h(x)$.