Just as in most programming languages like C++ all TI calculators have an atan2() function. It's just hidden away.
For the equation: atan2(x,y) use

Code:
R►Pθ(y,x)


Example: tan α = (cos ε sin L)/ cos L
Where ε = 23.43949 and L = 229.24429 degrees.
Solve: R►Pθ(cos L,cos ε sin L) = R►Pθ(cos(229.24429),cos(23.43949)sin(229.24429))
Result: -133.2085302 = 226.7914698 degrees

If you had used tan⁻() instead the result would have been 46.7914698 which is wrong by 180 degrees.
  
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