Is the dual of the space of section of a vector bundle Isomorphic to the space of section of the dual bundle?

Question

Let $(M, E, \pi, \cdot,+)$ be a vector bundle and let $(M, E^*, \pi, \times,*)$ be a the dual bundle. Denote $\Gamma(E)$ and $\Gamma(E^*)$ their respective space of section.

Now let $\Gamma(E)^*$ denote the dual of $\Gamma(E)$ .

Is $\Gamma(E)^*$ isomorphic to $\Gamma(E^*)$ ? If so how to proof this isomorphism ?