Using sed to substitute first occurrence

I am trying to get rid of some ending tags but I run into some problems.

Ex.

How are you?</EndTag><Begin>It is fine.</Begin><New> Just about

I am trying to get rid of the ending tags, starts with </ and ending with >. (which is </EndTag> and </Begin>)

I tried the following

sed 's/<\/.*>//g' file

It give me the following result which I did not want.
How are you? Just about.

It eliminated everything between you? and Just. There has to be a way to eliminate up to the first >

Second:

Same problem but split over two line.

How are you?</EndTag><Begin>It is fine.</Beg
in><New> Just about the same

Does anyone have an catchall sed command to eliminate everything from </... until it reaches the first > even though it expands mulitple lines.

Thank you.

sed by default is greedy and matches all instances of �>� up to the very last one on the line. Here is one way of only removing the content between "</" and ">":

$ cat file
How are you?</EndTag><Begin>It is fine.</Begin><New> Just about
$ sed 's/<\/[^>]*>//g' file
How are you?<Begin>It is fine.<New> Just about
$

Thanks, that seems to work on the first part.
But what about the 2nd part where the ending tag is split between two lines.
Sed seems to work when it is on one line but not when it is one two lines.

Ex.
</Beg
in>

Still haven't figure that part out.