Final answer:
The dimensionless theta equation is dimensionally consistent because the dimensions of both the left expression and the right expression are the same.
Step-by-step explanation:
The dimensionless theta equation is a mathematical expression where the argument is dimensionless. To prove the equation is dimensionless, we need to check the dimensions of each term. In this case, both the left expression and the right expression have the dimension [v] = LT-1. Since the dimensions of both terms are the same, the equation is dimensionally consistent.