How to solve an equation with one unknown and both sine and cosine

I am trying to solve an equation for a theta value. The theta is th eonly unknown and it appears in both a sine and a cosine function. An example of an equation I am trying to solve looks like this:

3.0179 = 6*cos(theta) - 2*sin(theta)*0.8660254038

I know that theta must equal 45 or 315 degrees. But when I use solve(), I get this answer:

-log((2989227959^(1/2) - 30179i)/(10000*(3^(1/2) - 6i)))*1i

-log(-(2989227959^(1/2) + 30179i)/(10000*(3^(1/2) - 6i)))*1i

How can I go about solving this equation for theta?

Answer 1

[Star Strider]

Try this —

syms theta 
Eqn = 3.0179 == 6*cos(theta) - 2*sin(theta)*0.8660254038

Eqn = 

theta = solve(Eqn, theta)

theta = 

thetav = vpa(theta, 9)

thetav = 

format long
thetad = double(theta)

thetad = 2×1

-1.347467201093442 0.785397398078239

.