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#TI-BASIC, 13 bytes
For TI-83+/84+ series calculators.
Degree Input Y min(ΔList(R►Pθ(Ans,∟Y
To use this program, enter the list {x1,x2} through the Ans variable, and {y1,y2} at the prompt.
{x1,x2}
{y1,y2}
