Tim T. answered • 05/02/19

Math: K-12th grade to Advanced Calc, Ring Theory, Cryptography

Greetings! Lets solve this shall we ?

So the equation we have is

tan(2θ/3) = - √3...............We must find all values of theta in radians such that this holds true. Then, we begin to solve by taking the inverse tangent to both sides such that

2θ/3 = tan^{-1}( -√3)..............Note that θ = tan^{-1}(-√3) = 2π/3 and 5π/3..............Then we solve for theta using both of these such that

2θ/3 = 2π/3

θ = 2π/3 (3/2)

**θ = π**..............This is one of the theta values

Now we solve for theta such that

2θ/3 = 5π/3

θ = 5π/3 (3/2)

**θ = 5π/2**

I hope this helped!