The hexa-2,4-diene stereoisomer shown is drawn with a definite geometry at both double bonds. Which of the following statements are correct?

In the drawing the C2=C3 bond has the C2 methyl and C4 on opposite sides, $(E)$, while the C4=C5 bond has C3 and the C5 methyl on the same side, $(Z)$: the compound shown is $(2E,4Z)$. Because the two ends of $\mathrm{CH}{}_3\mathrm{CH}=\mathrm{CH}-\mathrm{CH}=\mathrm{CHCH}{}_3$ are identical, numbering from the other end turns the same molecule into $(2Z,4E)$, so these names describe one compound. The distinct isomers are therefore $(E,E)$, $(Z,Z)$ and $(E,Z)$: 3 in total. All are planar and have a mirror plane, so none is chiral.