Find all values of theta in the interval 0 degree 360 degree

Find all values of theta in the interval [0 degree, 360 degree) have the given function value. tan theta = - Squareroot 3 theta =

First wr find reference angle by solving
tanR = +sqrt(3)
which we know results in
R = 60

Reference angle is always a positive acute angle

But we had to find tan(theta) = NEGATIVE sqrt3

Now, we know that tan is negative in quadrants 2 and 4 using sohcahtoa rule

So, using ref angle pi/3
we have to find the corresponding
angles in quadrants 2 and 4

Quad 2 angle = 180 - R = 180 - 60 = 120

Quad 4 angle = 360 - R = 360 - 60 = 300

So, answers are :
120 and 300