Using the Z - Y - X (alpha - beta - gamma) Euler angle convention, write a MATLAB program to calculate the rotation matrix _B^A R when the user enters the Euler angles alpha -beta -gamma. Test for two examples: i. alpha = 10 degree, beta = 20 degree, gamma = 30 degree. ii. alpha = 30 degree, beta = 90 degree, gamma = -55 degree For case (i), demonstrate the six constraints for unitary orthonormal rotation matrices (i.e., there are nine numbers in a 3 times 3 matrix, but only three are independent). Also, demonstrate the property, _A^B R = _B^A R^-1 = _B^A RT, for case (i)