The first thing I would try is to set your common headers for your http requests that angular dispatches, by inserting the following config block on your module:
.config(function($httpProvider){
$httpProvider.defaults.headers.common = {};
$httpProvider.defaults.headers.post = {};
$httpProvider.defaults.headers.put = {};
$httpProvider.defaults.headers.patch = {};
})
These are supposed to be set by default already, but I've found that I often have to do this manually in my config due to any overrides from other modules or internal angular bootstraping process.
Your CORS filter should be enough on the server side to allow these types of requests, but sometimes, you need to specify request methods in addition to your origins, as well as accepted content types. The tomcat docs have this advanced block, which addresses those.
<filter>
<filter-name>CorsFilter</filter-name>
<filter-class>org.apache.catalina.filters.CorsFilter</filter-class>
<init-param>
<param-name>cors.allowed.origins</param-name>
<param-value>*</param-value>
</init-param>
<init-param>
<param-name>cors.allowed.methods</param-name>
<param-value>GET,POST,HEAD,OPTIONS,PUT</param-value>
</init-param>
<init-param>
<param-name>cors.allowed.headers</param-name>
<param-value>Content-Type,X-Requested-With,accept,Origin,Access-Control-Request-Method,Access-Control-Request-Headers</param-value>
</init-param>
<init-param>
<param-name>cors.exposed.headers</param-name>
<param-value>Access-Control-Allow-Origin,Access-Control-Allow-Credentials</param-value>
</init-param>
<init-param>
<param-name>cors.support.credentials</param-name>
<param-value>true</param-value>
</init-param>
<init-param>
<param-name>cors.preflight.maxage</param-name>
<param-value>10</param-value>
</init-param>
</filter>
<filter-mapping>
<filter-name>CorsFilter</filter-name>
<url-pattern>/*</url-pattern>
</filter-mapping>
If the first doesn't work on it's own, try enhancing your filters, especially:
<init-param>
<param-name>cors.allowed.methods</param-name>
<param-value>GET,POST,HEAD,OPTIONS,PUT</param-value>
</init-param>
<init-param>
<param-name>cors.allowed.headers</param-name>
<param-value>Content-Type,X-Requested-With,accept,Origin,Access-Control-Request-Method,Access-Control-Request-Headers</param-value>
</init-param>
<init-param>
<param-name>cors.exposed.headers</param-name>
<param-value>Access-Control-Allow-Origin,Access-Control-Allow-Credentials</param-value>
</init-param>