RIGHT TRIANGLE TRIGONOMETRY

I encountered a problem with this explanation: Since tan 45° is always equal to 1, it follows that θ= 45°

The instructor also said these are shortcuts you have to memorize but I can't seem to find a complete list of these equivalents. I've been having a difficult time answering problems related to this because I can figure out the equivalent degree. Is there actually a way to solve this? Like maybe a reverse solution.