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R1:=matrix([[cos a, sin a, 0],[-sin a, cos a, 0],[0, 0, 1]])

R2:=matrix([[cos b, 0, -sin b],[0, 1, 0],[sin b, 0, cos b]])

R:=R2*R1

V:=matrix([[x1],[y1],[z1]])
E:=R*V=V

F:=lhs(E)-rhs(E)

G:=F=matrix([[0],[0],[0]])

H:=elt(F,2,1)

x1:=k

J:=subst(H,'x1=k)

L:=solve(J,y1)

y1:=rhs(first(solve(J,y1)))

H1:=elt(F,3,1)

J1:=subst(H1,['x1=x1, 'y1=y1])

z1:=simplify(rhs(first(solve(J1,z1))))

[x1,y1,z1]

y1:=eval(y1,[k=-1])

z1:=eval(z1,[k=-1])

[x1,y1,z1]

RSQ:SQMATRIX(3,EXPR(INT)):=R

TR:=trace(RSQ)

TREQ:=TR=1+2*cos(c)

c:=rhs(first(solve(TREQ,c)))

x1v:=eval(x1,k=-1)

y1v:=numeric(eval(y1,[a=%pi/6]))

z1v:=numeric(eval(z1,[k=-1,b=%pi/3]))

[x1v, y1v, z1v]

c1v:=numeric(eval(c,[a=%pi/6,b=%pi/3]))

c1v*180/%pi

rv:=eval(R,[a=%pi/6,b=%pi/3])