Question on transformed tan function (about my notes - not involving a problem)

Under "Properties of the transformed tangent function #3," I don't get the notation for the domain. Can someone elaborate in great detail for me please?

Thanks in advance!

Hi

It means that the domain is except the set of reals x such that there exists such that

In other words, everywhere except where the argument of tangent is an odd multiple of , since tangent is not defined there.