I can succesfully install trinity using

deb http://mirror.xcer.cz/trinity-sb trusty deps-r14 main-r14
deb-src http://mirror.xcer.cz/trinity-sb trusty deps-r14 main-r14

sudo aptitude install kubuntu-default-settings-trinity kubuntu-desktop-trinity

However when i use the official sites

deb http://mirror.ppa.trinitydesktop.org/trinity/trinity-r14.0.0/ubuntu trusty main
deb-src http://mirror.ppa.trinitydesktop.org/trinity/trinity-r14.0.0/ubuntu trusty main
deb http://mirror.ppa.trinitydesktop.org/trinity/trinity-builddeps-r14.0.0/ubuntu trusty main
deb-src http://mirror.ppa.trinitydesktop.org/trinity/trinity-builddeps-r14.0.0/ubuntu trusty main

I obtain

npacking kubuntu-default-settings-trinity (4:14.0.3-0ubuntu14.04.0+0) ...
dpkg: error processing archive /var/cache/apt/archives/kubuntu-default-settings-trinity_4%3a14.0.3-0ubuntu14.04.0+0_all.deb (--unpack):
trying to overwrite '/etc/kde4rc', which is also in package kubuntu-settings-desktop 1:14.04ubuntu15.1
dpkg-deb: error: subprocess paste was killed by signal (Broken pipe)
Unknown argument (abort-install) for /var/lib/dpkg/tmp.ci/postrm
Errors were encountered while processing:
/var/cache/apt/archives/kubuntu-default-settings-trinity_4%3a14.0.3-0ubuntu14.04.0+0_all.deb
E: Sub-process /usr/bin/dpkg returned an error code (1)
A package failed to install. Trying to recover:

I reported a similar error a while ago and I am puzzled that it is still exist, out of curiosity I will try 16.04 official

Uwe Brauer