Some countries only issue visa only in your home country or country of residence at that point if it is different from your home country. For example, you cannot apply and be issued with for a shengen when already in the UK if wishing to travel to the continent.
Unless the Ethiopian embassy categorically states that you can apply and be issued with a visa in a 3rd country - Nairobi embassy in this case, you are advised to wait it out here at home.
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