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I dont know very well.
You can start with calculating the s-parameters of the coupler first. Then, you may send 1 ∠0 into Port1 and solve for the reflected wave. Once you find the reflected wave, you can calculate the reflection coefficient and the input impedance.
By the way, the input impedance there is not something considered even or odd, it does not make sense for me.
You have loads at the other ports, I think we can not mention even/odd modes anymore.
Have you heard of commensurate lines, the line lengths should be fixed somewhere for convenience, you may fix it corresponding to quarter-wavelength. Otherwise, hand-calculation may become exhausting.
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