this diagram conveys a lot of information
you can find sin, cos and tan of 30, 60 and 45 degrees in surd (exact) form
but you can also, with a bit of work, find sin, cos and tan of 15 and 75 degrees in surd form
simplification requires rationalising the denominator
given some information about tan 15 and tan 75, you can find them in surd form:
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