Abstract: The method of how to obtain the representation matrix of rotation operation with respect to Euler angles was reviewed. New formulae of Euler angle related to rotating φ around arbitrary axisμ are deduced according to cosine theorem, simple geometry relations and character theory of group. Euler angles related to rotating 2π/3 around line which passes origin and （1,1,1） are obtained employing the obtained expressions.

Key words: Euler angles, direction cosine, group representation, character of group