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For such complicated functions you can use FindRoot over a range of your parameters to get an idea. data = Flatten[Table[{10^8 l, 10^8 d, f0 /. FindRoot[l == 6.79018*10^-9/f0 - (2.16138*10^-9 ArcTan[Sqrt[Tan[4.62667*10^8 d f0]^2]])/f0, {f0, 0.5}]} , {l, 2. 10^-8, 50. 10^-8, 10^-8}, {d, 2. 10^-8, 50. 10^-8, 10^-8}], 1]; ListPlot3D[data, AxesLabel -...


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Updated based on the following formulas provided as additional clarification: Beta = 2 Pi / Lambda = 2 Pi Sqrt[4.88] f / c Z0 = 50 and ZL>>Z0 Solved: Solve[{dvar == 1/((2 Pi)/wL) ArcTan[Sqrt[ZL/50]], lvar == wL/2 - 1/((2 Pi)/wL) ArcTan[(ZL)/Sqrt[ZL 50]]}, {wL, ZL}] {{wL -> 2*(dvar + lvar), ZL -> 50 Tan[(dvar Pi)/(dvar + lvar)]^2}} v = ...


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Example how to factor a trigonometric expression



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