How to show sinα - sinβ = 2cos((α+β)/2)sin((α-β)/2)

In this video I work through how to show:
sinα - sinβ = 2cos((α+β)/2)sin((α-β)/2)
I use two compound angle formulas plus a neat trick to go from α and β to a combination of (α+β)/2 and (α-β)/2.
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