The "similarity" is not coincidental; the vowel found in words like "care" is often transcribed as /eə/ because, historically, many people pronounced it like the sound [e] followed by the sound [ə], squished into one syllable. (The non-syllabic part was the [ə]; a more explicit transcription would be /eə̯/.) However, in modern Southern British speech, words like "care" are often pronounced with a long monophthong rather than a centering diphthong due to the phenomenon of "smoothing", so it may be better for you to aim for /ɛː/; at any rate, you should be aware of the existence of this pronunciation.
Here is a blog post about it by Geoff Lindsey: Smoothing, then and now