# Uniquity of an Equilateral

Geometry Level 4

Two lines $$l_1$$ and $$l_2$$ intersect at an angle of $$\theta$$. A point $$P$$ is randomly chosen in the same plane as the two lines. If there is exactly one equilateral triangle with one vertex as $$P$$, one vertex on $$l_1$$, and one vertex on $$l_2$$, then find the sum of all possible values of $$\theta$$.

Details and Assumptions

$$0\le \theta \le 90^{\circ}$$

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