When a child throws a tantrum, and the parents are frustrated and don't know how to manage it, the kid feels insecure, as he counts on the parents on being strong unmovable pillars of stability. The best response is for the parent to be Stoic. Have clear boundaries, including boundaries of how he is allowed to express his frustrations (and what is not ok). Let him express his frustrations in this acceptable context.
For example, when my son throws a tantrum, I validate the reason for his frustration, sometimes I can get him to talk about why he is frustrated. He knows that if he doesn't communicate in a way I understand, nothing will get done as he wants. I just ask him repeatedly to calm down and tell me in a way I understand. If he doesn't do it, I count 1,2,3, and enforce the consequence. He knows the count, so he calms down usually by 2, and we sit down and talk for a bit. This takes a lot of time and flexibility on my part.
An important thing is to be clear to myself about the difference between "I need him to do X" and "I want him to learn X." Confusing them is MY own fault, and leads to bad parenting. I find that more often than not, if I'm flexible and budget time, i can focus on teaching moments for him. If you try to do both (Get him to do X in the same instance you are trying to teach him the importance of X) you get frustrated, and give a confusing message, which makes the tantrum worse.
This is hard work, there is no magical aphorism you can tell them so they pursue virtue. However, you acting Stoic models how to process frustrations. They do see what you do. In fact, tantrums often are their way of testing this, by seeing how you deal with their frustration, they learn how they themselves deal with them.
One time my son was frustrated he couldn't build a cool lego airplane he wanted... the parts kept coming apart. he yelled in frustration. He knew by then that if he did that, i wouldn't help him. if he asked nicely, i would. so i gave him the look "hey buddy, is there a problem? what's up with this tone?" and he told me he needed space, he said he needed to be alone. He sat on the floor of his room, breathed deeply for a bit, and I let him doing other things around the house (while keeping my ear attentive). Then he came out of his room saying he felt better now and was behaving well, and now he wanted to play with me. This was a big victory for him.
In the end, in a tantrum the kid has a lot of control about his chaos. If you fight for that control, you empower the tantrum even more. Don't try to change the kid. Change your actions, and the kid will follow.
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