<Tri-2025-2214>, hint

Since AB//OD, <ODM=<B   M is the midpoint of BC  R is the radius of circumcircle  ofABC

BM=BD+MD   <-->R sinA=2R sinC cos B+R cos A cot B

cos(B+C)=cosBcosC-sinB sinC, sin2B=2sinB cosB, cotB= cosB/sinB, cos(B+C)=-cosA

sinA=2sinC cosB+cosA cot B --->> sin2B=cotC