Prove that $~ 60 ^{\circ} ~$ is taken in the parallelogram which takes $~ 60 ^{\circ} ~$ at bottom left and the top left

Question

I've drawn the below diagram .

I have to prove that the $~ \theta_{} ~$ takes $~ 60 ^{\circ} ~$

I 've written the angles in the above diagram which I found so far .

Hints are needed .

Answer 1

From the symmetry of the rhombus , the angle which is halved by the diagnol line is 60 degrees.