Game Winning Three

Suppose you're taking a three point shot at a basket that's $11 \text{ m}$ down the court, and $1.15 \text{ m}$ above your head. You can take the shot at any angle you like, however, you're not perfect and you're likely to imperfectly set your release angle.

What release angle $\theta$ (in degrees) should you aim for in order to maximize your chance of hitting the three pointer? (In other words, what release angle provides you with the biggest margin of error?)

Give your answer to 3 decimal places.

Details and Assumptions:

• Neglect wind resistance.
• Assume that you aim for the center of the basket.