trigonometric relations

1. simplify cos(90-θ)/(sin^2θtan(90-θ))
Sol
cos(90-θ)/(sin^2θtan(90-θ))
= sinθ/(sin^2θcotθ)
= 1/(sinθcotθ)
=1/cosθ
=secθ

2.given that cos(90-θ)/(sin^2θtan(90-θ))=1/sin4θ , find θ.
Sol
cos(90-θ)/(sin^2θtan(90-θ))=1/sin4θ
secθ=1/sin4θ
secθsin4θ=1
cosθ=sin4θ
cosθ=cos(pi/2-4θ)
θ=2npi+pi/2-4θ or θ=-2npi-pi/2+4θ n is integer
5θ=2npi+pi/2 or 3θ=2npi+pi/2+4θ n is integer
θ=(2npi+pi/2)/5 or θ=(2npi+pi/2+4θ)/3 n is integer