For real numbers $\theta_1, \theta_2, ...,\theta_11$ satisfying $$\sum^{11}_{i=1}\sin(\theta_i) = 1.$$The minimum value of $$\sum^{11}_{i=1}\sin(3\theta_i)$$is $-\frac{a}{b}$ where a, b are positive integers and gcd$(a, b) = 1$. Enter $a - b$.
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Tags: algebra, inequalities, trigonometry
For real numbers $\theta_1, \theta_2, ...,\theta_11$ satisfying $$\sum^{11}_{i=1}\sin(\theta_i) = 1.$$The minimum value of $$\sum^{11}_{i=1}\sin(3\theta_i)$$is $-\frac{a}{b}$ where a, b are positive integers and gcd$(a, b) = 1$. Enter $a - b$.