Considering that a is in Θ(c) and b is in Θ(d)

I need to prove that (a + b) is in Θ(max{c, d }).

How can I do it?

I tried to prove big o and big omega for both cases and then conclude big theta, but failed miserably...

I read a previous post here in which somebody recommended changing max c,d for a new variable e, but I still failed...

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