Acute Triangle Probability
A random number \( \theta \) is picked uniformly from \( (0, 180) \). Then, a random number \( \phi \) is picked uniformly from \( ( 0 , 180 - \theta ) \). Consider the triangle which has \( \theta \) and \( \phi \) as two of its angles. To the nearest tenth of a percent, what is the probability that this triangle is acute?
Details and Assumptions: If your answer is 12.3%, write 12.3 in the box.