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Quick way to return the boundaries of an inequality?

I'm doing some rather involved computations which end up with "Reduce"
results that look like:
1.0848 <= \[Theta] <= 1.18296 || 3.64861 <= \[Theta] <= 3.70078
Sometimes there will be two allowed regions, sometimes only one.  I
need a quick function/routine that will simply return me the
boundaries.  Basically I have to look for the maximum of a function of
Theta and know that it's monotonic over the intervals of interest.  So
I'd prefer to save myself some computation and just check the
endpoints.  Anyone know of a simple routine that would accomplish
this?  I can't think of anything straightforward that wouldn't involve
resolving things and undermining the whole idea of cutting
computational steps.

Thanks in advance,

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