Question

If \( \triangle A B C \) having vertices \( A\left(a \cos \theta_{1}, a \sin \theta_{1}\right), B\left(a \cos \theta_{2}\right. \), \( \left.a \sin \theta_{2}\right) \), and \( C\left(a \cos \theta_{3}, a \sin \theta_{3}\right) \) is equilateral, then prove that \( \cos \theta_{1}+\cos \theta_{2}+\cos \theta_{3}=\sin \theta_{1}+\sin \theta_{2}+\sin \theta_{3}=0 \).

Answer 1

https://www.sarthaks.com/?qa=blob&qa_blobid=7822077155213907764

△ ABC is equilateral 

So Circumcenter (O), Orthocenter(H) and Centroid(G) are same