A Geocaching race organizer is putting four caches along a route that starts and finishes at the same place.
While making his route, he recorded a few route details. Starting from point \(A\), the organizer travelled due west to point \(B\). From point \(B\), he travelled \(1500\) m southeast to point \(C\). While at \(C\), he noted that \(\angle BCA\) is \(45\degree\). From point \(C\), he travelled \(1000\) m in a direction \(30\degree\) north from east to point \(D\). Finally from point \(D\), he travelled due north to point \(E\) and noted that \(\angle DEC=30\degree\).
Determine the distance, rounded to the nearest metre, from the cache at point \(E\) to the race finish at point \(A\).