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So i know that argument of E must be equal to argument of U, since U is the voltage on inductor argument of the current through the inductor (let's call it I) is arg(I) = arg(U) - π/2.

Now, in order to find argument of E i could find the equivalent impedance of the circuit. I will start with the coupled inductors:

voltage on the inductors is U1=IjωL + IjωL12 + IjωL + IjωL12, since k=1 then L12=L so U1=Ij4ωL, so impedance of these two inductors is Z1=j4ωL, arg(Z1)=π/2, and it's in parallel with capacitor so Z2=[j4ωL*(1/jωC)]/(j(4ωL-1/(ωC))

Z2=4L/[jC(4ωL-1/(ωC))] but now i don't know what happens with argument of Z2, i mean i should somehow express argument of E but to do that, i should find the argument of Z2, but i don't know how. Is this correct approach?