17.79 USE problems
condition: Prove that for any \( p \) and \( t \) the inequality \( 2(2 p-1)^{4}+1+(1-2(2 p- \) \( \left.-1)^{4}\right) \sin 2 t \geq 0 \), and find all pairs \( (p, t) \), at which it turns into equality.
Problems of the USE (Unified State Exam) - equations and inequalities in terms of a parameter, solved both by algebraic methods and geometric ones.