Months passed as Rui patiently adhered to his word. He didn't want to waste any more time in the Garden of Salvation than absolutely necessary. The Elder Tree was thankfully intelligent, learning math and science at a remarkable speed.
I don't understand this problem.
The Elder Tree projected the numerical into Rui's head. It was an elementary trigonometric equation that required simplification.
"It's simple," Rui patiently informed it. "Apply the expressions sine-two-theta equals two sine-theta-cos-theta, and cos-two-theta equals cos-squared-theta minus sin-squared-theta. Once the angles of the trigonometric terms are equal, you can cancel them out, and you'll be left with a simplified expression."
I see. That does indeed solve the problem.
Rui ensured that the quality of the education that he imparted to the Elder Tree was high so that the rate of learning and time period required to learn everything he needed to know was high.