How do you find the exact value of ##tan ((pi)/2)##?

It does not have an exact value as it is undefined and diverges to ##oo##.

The graph of ##y=tanx## has a vertical asymptote at ##x=pi/2## and so the limit ##lim_(x->pi/2)tanx## does not exist. The graph diverges to ##oo## as x approaches ##pi/2##.

graph{tanx [-8.89, 8.89, -4.444, 4.45]}