Question: User: Again, note that $8.04 = \frac{804}{100} = \frac{201}{25}$. Multiply by $\frac{25}{201}$ to solve for $\theta$. $\frac{107\pi}{80} = \frac{201}{25} \theta$ $\frac{\square}{3216} = \theta$ Solve for $\theta$. (type an exact answer, using $\pi$ as needed.)

1. **State the problem:** We are given the equation $$\frac{107\pi}{80} = \frac{201}{25} \theta$$ and need to solve for $\theta$. We also have $$\frac{\square}{3216} = \theta$$ and want to find the exact value of $\theta$. 2. **Isolate $\theta$:** To solve for $\theta$, multiply both sides of the first equation by the reciprocal of $\frac{201}{25}$, which is $\frac{25}{201}$: $$\theta = \frac{107\pi}{80} \times \frac{25}{201}$$ 3. **Simplify the expression:** $$\theta = \frac{107 \times 25 \times \pi}{80 \times 201}$$ 4. **Calculate numerator and denominator:** Numerator: $107 \times 25 = 2675$ Denominator: $80 \times 201 = 16080$ So, $$\theta = \frac{2675\pi}{16080}$$ 5. **Simplify the fraction $\frac{2675}{16080}$:** Find the greatest common divisor (GCD) of 2675 and 16080. - $2675 = 25 \times 107$ - $16080 = 80 \times 201$ Check common factors: - 25 divides 2675, and 80 divides 16080. Divide numerator and denominator by 5: $$\frac{2675}{16080} = \frac{\cancel{5}535}{\cancel{5}3216}$$ Divide numerator and denominator by 5 again: $$\frac{535}{3216}$$ No further common factors (535 factors: 5, 107; 3216 factors: 2, 3, 7, 23), so fraction is simplified. 6. **Final simplified expression for $\theta$:** $$\theta = \frac{535\pi}{3216}$$ 7. **Relate to the second equation:** Given $$\frac{\square}{3216} = \theta$$, comparing with above, we see: $$\square = 535\pi$$ **Answer:** $$\theta = \frac{535\pi}{3216}$$