Doug C. answered • 10/13/16

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My guess is the intent of this problem was to use trig identities for tan (x+y) and tan 2x.

tan(2x+pi) = (tan2x + tan pi)/(1-tan2xtanpi), Since tan pi = 0 we have this reducing to tan2x.

But tan2x = 2tanx/(1-tan

^{2}x). But from the diagram we know tanx = 3/4 (using x instead of theta),Substituting 3/4 for x in last, gives 2(3/4)/(1 - (3/4)

^{2}) = 3/2 / 7/16 or 24/7.