Solving for theta I am trying to solve some a math problem in a 3D software project.
I know that:
$$\cos(\theta)\sin(75°)a+\cos(75°)b+\sin(\theta)\sin(75°)c=0$$
How do I write an equation to solve for $\theta$? Could someone go through all the steps please? Because I have to solve many similar problems.
I already know that there may be zero, one, or (usually) two solutions.
Thanks.
[edit]
By the way, what would the solutions for $\theta$ be in this case if a = 4, b = 5, and c = 6? (Just so I can work it out on my own.)

HINT: Notice the common factor of $\sin(75^\circ)$. Write
$$a\cos\theta + c\sin\theta = \sqrt{a^2+c^2}\left(\frac a{\sqrt{a^2+c^2}} \cos\theta + \frac c{\sqrt{a^2+c^2}}\sin\theta\right).$$
There is an angle $\tau$ with
$$\cos\tau = \frac c{\sqrt{a^2+c^2}} \quad\text{and}\quad \sin\tau=\frac a{\sqrt{a^2+c^2}}.$$
Now you can use the addition formula for $\sin$ to express the term in parentheses as $\sin(\theta+\tau)$.
