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Math Prize 2019 Problem 15

Source:

October 15, 2019
Math Prize for Girls

Problem Statement

How many ordered pairs (x,y)(x, y) of real numbers xx and yy are there such that −100π≤x≤100π-100 \pi \le x \le 100 \pi, −100π≤y≤100π-100 \pi \le y \le 100 \pi, x+y=20.19x + y = 20.19, and tan⁡x+tan⁡y=20.19\tan x + \tan y = 20.19?
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