#f theta ) =csc 2theta + sin 4theta + cos 4theta#
#= 1/sin (2theta) + 2 sin 2theta cos 2theta#
#+ (cos^2 2theta - sin^2 2theta)#
#= 1/( 2 sin theta cos theta ) #
#+ 4 sin theta cos theta ( cos^2theta - sin^2theta)#
#+ (cos^2theta - sin^2theta )^2 - 4 sin^2theta cos^2theta#
#= 1/( 2 sin theta cos theta ) #
#+ 4 sin theta cos theta ( cos^2theta - sin^2theta)#
#+ (cos^2theta + sin^2theta )^2 - 6 sin^2theta cos^2theta#
#= 1/( 2 sin theta cos theta ) #
#+ 4 sin theta cos theta ( cos^2theta - sin^2theta)#
#+ 1 - 6 sin^2theta cos^2theta#
#= 1/( 2 sin theta cos theta ) #
#+ 2 sin theta cos theta ( 2 ( cos^2theta - sin^2theta )- 3 sin theta cos theta ) + 1#