Failure to simplify trig functions of simple rational multiples of %pi

Dear All,

Appended below is an Axiom input script whose last two lines (the
subst() and solve()) produce output involving cos(%pi/2), sin(%pi/2),
and sin(%pi), which I'd naively expect to be automatically simplfied
to 0, 1, and 0 respectively.  How can I get this automatic
simplification to happen, please?

Thanks,

Dan

l:Union(Variable l,Integer)
m:Union(Variable m,Integer)
n:Union(Variable n,Integer)

A :=  a*sin(l*%pi*x)*cos(m*%pi*y)*cos(n*%pi*z)
B :=  b*cos(l*%pi*x)*sin(m*%pi*y)*cos(n*%pi*z)
C :=  c*cos(l*%pi*x)*cos(m*%pi*y)*sin(n*%pi*z)
D :=  d*cos(l*%pi*x)*cos(m*%pi*y)*sin(n*%pi*z)

E :=  e1*cos(l*%pi*x)*cos(m*%pi*y)*sin(n*%pi*z)+(e2+e3*cos(2*l*%pi*x)+e4*cos(2*m*%pi*y))*sin(2*n*%pi*z)
F :=  f1*cos(l*%pi*x)*cos(m*%pi*y)*sin(n*%pi*z)+(f2+f3*cos(2*l*%pi*x)+f4*cos(2*m*%pi*y))*sin(2*n*%pi*z)

A*differentiate(D,x)+B*differentiate(D,y)+C*differentiate(D,z)-E-differentiate(F,x,2)-differentiate(F,y,2)-differentiate(F,z,2)  = 0

subst(%,z = 1/(2*n))

solve(%,f1)