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Arctan(tan(2pi/3))

i know it looks like the short cut is applicable here. But isn't there a second point on the unit circle with the same tangent as 2pi/3? Tan(2pi/3)= -(Sqr.rt. 3) There are other places with the same value for tangent. 5pi/3 Tan(5pi/3)= -(Sqr.rt. 3)

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Arctan(tan(2pi/3))

i know it looks like the short cut is applicable here. But isn't there a second point on the unit circle with the same tangent as 2pi/3? Tan(2pi/3)= -(Sqr.rt. 3) There are other places with the same value for tangent. 5pi/3 Tan(5pi/3)= -(Sqr.rt. 3)