Question: Trigonometric Simplifications

How to make Maple recognize that: sin(x) +sin(x+Pi/3) is equivalent to sqrt(3)sin(x+Pi/6), and various variants of this expression involving sine, cosine, constants equal to Pi/3, Pi/6, etc? I can do it using the subs finction, but this involves finding the equivalent by hand for each variant. Thanks.

 

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