How to find the first three positive values of $\theta=\arctan(3)$? How would I find the first three positive values of that? All I know is that the equation can also be written as $\theta=\arctan(3)$
 A: Note that the tangent function is postive in Quadrant I and III. Now every trigonometric have only one, unique value in each quadrant, which means only one angle in quadrant I satisfy your equation, also it's case in the third.
In the first quadrant the angle $\theta$ that satisfy your equtaion is: 71,56 degrees. This is the first one. Now we know that if we add 360 degrees we'll get the same tangent value for the angle so the general equation for the angles in Quad. I is
$$\theta = 360k + 71.56\text {; k=1,2,3...}$$ 
Know to get the value for Quad. III we add 180 to the value from the Quad. I and the general equation is:
$$\theta = 360k + 251.56\text {; k=1,2,3...}$$ 
And from these equation we get that angles that satisfy your equation can be written as:
$$\theta = 180k + 251.56\text {; k=1,2,3...}$$
$$\text{ or in radians}$$
$$\theta = k\pi + 1.25\text {; k=1,2,3...}$$
And if you are interested in generating trigonometric function I recommend you using the Taylor-Maclaurin Series.I use it and it's one of the easiest way to generate values for trigonometric function
