If $tan (α) = 2$ and $tan (β) = 3$ , what is $tan (α + β)$ ?

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In $△ A B C$ , $b = 5$ , $c = 8$ , and $∠ A = 6 0^{\circ}$ . What is the exact length of side $a$ ?
Calculate the area of $△ A B C$ where side $a = 6$ , side $b = 10$ , and $∠ C = 3 0^{\circ}$ .
If $sin (θ) + cos (θ) = \frac{7}{5}$ for an acute angle $θ$ , what is the value of $sin (2 θ)$ ?
According to the Law of Sines, in $△ A B C$ with $a = 12$ and $∠ A = 3 0^{\circ}$ , what is the radius $R$ of the circumcircle?
Simplify the trigonometric expression: $\frac{1 - c o s ( 2 θ )}{s i n ( 2 θ )}$ .