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Add some conversions for a,b,c alpha beta gamma

a = 1
b = 2
c = 3

alpha = 90
beta = 90
gamma = 90

def cos(theta):
    return np.cos(np.deg2rad(theta))

def acos(theta):
    return np.rad2deg(np.acos(np.deg2rad(theta)))

def sin(theta):
    return np.sin(np.deg2rad(theta))

def asin(theta):
    return np.rad2deg(np.acos(np.deg2rad(theta)))
                     
metric_tensor = np.array([[a**2,           a*b*cos(gamma), a*c*cos(beta)],
                          [a*b*cos(gamma), b**2,           b*c*cos(alpha)],
                          [a*c*cos(beta), b*c*cos(alpha),  c**2]])

v1 = [1, 0, 0]
v2 = [1, 1, 1]

dot_product_v1_v2 = np.dot(v1, np.dot(metric_tensor, v2))

reciprocal_tensor = np.transpose(np.linalg.inv(metric_tensor))

alpha_star = asin(reciprocal_tensor_for_angles[1, 2]/(b_star*c_star))
beta_star = asin(reciprocal_tensor_for_angles[0, 2]/(a_star*c_star))
gamma_star = asin(reciprocal_tensor_for_angles[0, 1]/(a_star*b_star))

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