import sympy as sym
x,y,z = sym.symbols('x,y,z') 
r = sym.sqrt(x**2+y**2+z**2)
theta = sym.acos(z/r)
phi = sym.acos(x/sym.sqrt(x**2+y**2))
coor = sym.Matrix([r, theta, phi])
xyz = sym.Matrix([x, y, z])
metric = sym.diag(1, r**2, r**2*sym.sin(theta)**2)
jac = coor.jacobian(xyz) 
print(sym.simplify(jac.T*metric*jac))