Calculate point coordinates having angle and length in 2d

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I am having a little geometry problem to solve and I have to say that my math is a little rusty. I've attached an image below, which explain visually my situation.

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I have the following information, coordinates of points W and Z, length of WA = AB = BZ and length WZ. I have the angle θ as well.

My question is, how can I calculate coordinates of points A and B?

Can anyone help me?

Thank you in advance.

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Unfortunately I cannot comment yet, but if you have to do such an operation more often, I would look into Rotation matrices. It will be beneficial in the future.

For now, can you calculate the length of $ZW$?