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use strict;
use warnings;
...

$tags{ uc $1 }++ while $tagged =~ m!<([^/]+?)>!g;
print "$_: $tags{$_}\n" for sort keys %tags;

<det>the</det> <jj>quick</jj> <jj>brown</jj> <nn>fox</nn> <vbd>jumped<
+/vbd> <in>over</in> <det>the</det> <jj>lazy</jj> <nn>dog</nn>

...
JJ: 3
NN: 2
VBD: 1