@acer Many thanks

eqns := {-theta[1, 2]*theta[2, 6]-theta[1, 3]*theta[3, 6]+1 = 0, theta[1, 2]*theta[2, 6]+theta[1, 3]*theta[3, 6]-1 = 0, -theta[1, 2]*theta[2, 6]*theta[3, 6]-theta[1, 3]*theta[3, 6]^2+1 = 0, -theta[1, 1]*theta[1, 2]*theta[2, 2]*theta[2, 6]*theta[3, 6]-theta[1, 1]*theta[1, 3]*theta[2, 2]*theta[3, 6]^2+1 = 0, -theta[1, 3]*theta[2, 2]+theta[1, 3]*theta[3, 3]+alpha+rho = 0, theta[1, 0]*theta[1, 3]*theta[2, 2]^2*theta[3, 3]-theta[1, 0]*theta[1, 3]*theta[2, 2]*theta[3, 3]^2-alpha^2*beta-alpha*beta*rho = 0, theta[1, 1]*theta[1, 2]*theta[2, 6]+theta[1, 1]*theta[1, 3]*theta[3, 6]+theta[1, 2]*theta[2, 2]*theta[2, 6]+theta[1, 3]*theta[2, 2]*theta[3, 6]-alpha = 0, theta[1, 1]*theta[1, 2]*theta[2, 6]*theta[3, 6]+theta[1, 1]*theta[1, 3]*theta[3, 6]^2+theta[1, 2]*theta[2, 2]*theta[2, 6]*theta[3, 6]+theta[1, 3]*theta[2, 2]*theta[3, 6]^2-alpha = 0, theta[1, 1]*theta[1, 3]*theta[2, 2]-theta[1, 1]*theta[1, 3]*theta[3, 3]+theta[1, 3]*theta[2, 2]^2-theta[1, 3]*theta[3, 3]^2-alpha^2+rho^2 = 0, -theta[1, 1]*theta[1, 2]*theta[2, 6]-theta[1, 1]*theta[1, 3]*theta[3, 6]-theta[1, 2]*theta[2, 2]*theta[2, 6]-theta[1, 2]*theta[2, 6]*theta[3, 3]-2*theta[1, 3]*theta[3, 3]*theta[3, 6]-2*rho = 0, -theta[1, 0]*theta[1, 2]*theta[2, 2]*theta[2, 6]*theta[3, 6]-theta[1, 0]*theta[1, 3]*theta[2, 2]*theta[3, 6]^2-theta[1, 1]*theta[1, 2]*theta[2, 2]*theta[2, 6]*theta[3, 3]+theta[1, 1]*theta[1, 3]*theta[2, 2]^2*theta[3, 6]-2*theta[1, 1]*theta[1, 3]*theta[2, 2]*theta[3, 3]*theta[3, 6]-alpha-2*rho = 0, theta[1, 1]*theta[1, 2]*theta[2, 6]*theta[3, 3]-theta[1, 1]*theta[1, 3]*theta[2, 2]*theta[3, 6]+2*theta[1, 1]*theta[1, 3]*theta[3, 3]*theta[3, 6]+theta[1, 2]*theta[2, 2]*theta[2, 6]*theta[3, 3]-theta[1, 3]*theta[2, 2]^2*theta[3, 6]+2*theta[1, 3]*theta[2, 2]*theta[3, 3]*theta[3, 6]+alpha^2+2*alpha*rho = 0, -theta[1, 0]*theta[1, 2]*theta[2, 2]*theta[2, 6]*theta[3, 3]+theta[1, 0]*theta[1, 3]*theta[2, 2]^2*theta[3, 6]-2*theta[1, 0]*theta[1, 3]*theta[2, 2]*theta[3, 3]*theta[3, 6]+theta[1, 1]*theta[1, 3]*theta[2, 2]^2*theta[3, 3]-theta[1, 1]*theta[1, 3]*theta[2, 2]*theta[3, 3]^2+alpha*beta+alpha*rho+rho^2 = 0, -theta[1, 0]*theta[1, 2]*theta[2, 2]*theta[2, 6]-theta[1, 0]*theta[1, 3]*theta[2, 2]*theta[3, 6]-theta[1, 1]*theta[1, 3]*theta[2, 2]^2+theta[1, 1]*theta[1, 3]*theta[3, 3]^2-theta[1, 3]*theta[2, 2]^2*theta[3, 3]+theta[1, 3]*theta[2, 2]*theta[3, 3]^2-alpha^2*rho-alpha*rho^2+alpha+beta+rho = 0}

and

fc := {theta[1, 0], theta[1, 1], theta[1, 2], theta[1, 3], theta[2, 2], theta[2, 6], theta[3, 3], theta[3, 6]}