Question 175821
tan 75 = tan (45 + 30).  tan (a + b) = (tan a + tan b)/(1 - tan a * tan b).  So your problem, tan 75 = tan (45 + 30) = (tan 45 + tan 30)/(1 - tan 45 * tan 30).

45 and 30 are special angles, so you should know them; tan 30 = {{{sqrt(3)}}}/3 and tan 45 = 1.  Just plug these in and solve!