Step 1: Scan the equation term by term for the highest derivative:
The terms present are $(d^2y/dx^2)^3$, $(dy/dx)^2$, $\sin(dy/dx)$ and a constant. The largest derivative order appearing anywhere is 2 (from $d^2y/dx^2$), so order $=2$.
Step 2: Try to write the equation as a pure polynomial:
A polynomial in $y', y''$ would only allow whole-number powers of these derivatives added together, never a derivative passed through a transcendental function like $\sin(\cdot)$. Expanding $\sin(dy/dx)$ as a Taylor series gives infinitely many powers of $dy/dx$, not a finite polynomial.
Step 3: Conclude:
Since the equation cannot be forced into polynomial form in the derivatives, the standard convention says the degree does not exist for this equation.
Final Answer:
Order is 2; degree is not defined.
\[ \boxed{\text{Order} = 2,\ \text{Degree not defined}} \]