sinΘ=0.955Θ

theta = 0 is another solution.

An approximate solution can be obtained quickly by noting that when theta is small then sin(theta) ≈ theta - theta^3/3!

This results in  theta - theta^3/6 = 0.955theta

theta(1 - 0.955 - theta^2/6) ≈ 0

1.   theta = 0

2.  theta^2 ≈ 0.27  so theta ≈ +/- 0.52

.

Take the Inverse sine or sin^-1 of 0.955,

So, theta=sin^-1(0.955) =~72.75 degrees.

theta = approximately     + or - 0.523

https://www.wolframalpha.com/input/?i=sin%CE%98%3D0.955%CE%98

" An approximate solution can be obtained quickly by noting that when theta is small then sin(theta) ≈ theta - theta^3/3!'

Note : Alan derives this from the first two terms of the Taylor Series for the sine function :

sin x = x − x 3 3! + x 5 5! − x 7 7! + x 9 9! − ....