We know that eclipse is when the Sun, the Earth and the Moon align in a straight line.
How do they do this align if their orbit planes aren't in the same angle?
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Planes intersect along a line. Normally we see a full Moon shining in Her fullness for exactly the reason you cite, but just sometimes the Moon passes through an intersection point exactly when occluded by the Earth and so we get a lunar eclipse. Swap the rôles of Moon and Earth and there's your answer.
They are not in the same plane, but the planes intersect, and the relative orientation goes through 360 degrees every 365.2524 days.
The objection would be valid if the lunar plane were parallel to the earth's plane, but offset by more than one Earth radius, but that is not how it works.
By the way, the alignment is call "syzygy".