Angle of a trapezium

Geometry Level 5

\(ABCD\) is a trapezium with \( AD \parallel BC \) and \(AB = AD \). \( 0^\circ < \theta < 180^\circ \) is an angle such that \( \angle BAC = \theta\), \( \angle CAD = 3 \theta \) and \( \angle ACD = 5 \theta \). What is the measure (in degrees) of \(\theta\)?

Details and assumptions